diff --git a/doc/whats_new/v1.1.rst b/doc/whats_new/v1.1.rst
index 1639b4b691c65..fba40e25a9e7e 100644
--- a/doc/whats_new/v1.1.rst
+++ b/doc/whats_new/v1.1.rst
@@ -38,9 +38,20 @@ Changelog
     :pr:`123456` by :user:`Joe Bloggs <joeongithub>`.
     where 123456 is the *pull request* number, not the issue number.
 
-
-:mod:`sklearn.decomposition`
-............................
+:mod:`sklearn.utils`
+....................
+
+- |Enhancement| :func:`utils.validation._check_sample_weight` can perform a
+  non-negativity check on the sample weights. It can be turned on
+  using the only_non_negative bool parameter.
+  Estimators that check for non-negative weights are updated:
+  :func:`linear_model.LinearRegression` (here the previous
+  error message was misleading),
+  :func:`ensemble.AdaBoostClassifier`,
+  :func:`ensemble.AdaBoostRegressor`,
+  :func:`neighbors.KernelDensity`.
+  :pr:`20880` by :user:`Guillaume Lemaitre <glemaitre>`
+  and :user:`András Simon <simonandras>`.
 
 
 Code and Documentation Contributors
diff --git a/sklearn/ensemble/_weight_boosting.py b/sklearn/ensemble/_weight_boosting.py
index 77ef449ba1933..a47937880d91c 100644
--- a/sklearn/ensemble/_weight_boosting.py
+++ b/sklearn/ensemble/_weight_boosting.py
@@ -123,10 +123,10 @@ def fit(self, X, y, sample_weight=None):
             y_numeric=is_regressor(self),
         )
 
-        sample_weight = _check_sample_weight(sample_weight, X, np.float64, copy=True)
+        sample_weight = _check_sample_weight(
+            sample_weight, X, np.float64, copy=True, only_non_negative=True
+        )
         sample_weight /= sample_weight.sum()
-        if np.any(sample_weight < 0):
-            raise ValueError("sample_weight cannot contain negative weights")
 
         # Check parameters
         self._validate_estimator()
@@ -136,7 +136,7 @@ def fit(self, X, y, sample_weight=None):
         self.estimator_weights_ = np.zeros(self.n_estimators, dtype=np.float64)
         self.estimator_errors_ = np.ones(self.n_estimators, dtype=np.float64)
 
-        # Initializion of the random number instance that will be used to
+        # Initialization of the random number instance that will be used to
         # generate a seed at each iteration
         random_state = check_random_state(self.random_state)
 
diff --git a/sklearn/ensemble/tests/test_weight_boosting.py b/sklearn/ensemble/tests/test_weight_boosting.py
index 6927d47c11cfe..159f83abf24c4 100755
--- a/sklearn/ensemble/tests/test_weight_boosting.py
+++ b/sklearn/ensemble/tests/test_weight_boosting.py
@@ -576,6 +576,6 @@ def test_adaboost_negative_weight_error(model, X, y):
     sample_weight = np.ones_like(y)
     sample_weight[-1] = -10
 
-    err_msg = "sample_weight cannot contain negative weight"
+    err_msg = "Negative values in data passed to `sample_weight`"
     with pytest.raises(ValueError, match=err_msg):
         model.fit(X, y, sample_weight=sample_weight)
diff --git a/sklearn/linear_model/_base.py b/sklearn/linear_model/_base.py
index 79d6f321cb124..8b5102ecdd403 100644
--- a/sklearn/linear_model/_base.py
+++ b/sklearn/linear_model/_base.py
@@ -663,7 +663,9 @@ def fit(self, X, y, sample_weight=None):
         )
 
         if sample_weight is not None:
-            sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype)
+            sample_weight = _check_sample_weight(
+                sample_weight, X, dtype=X.dtype, only_non_negative=True
+            )
 
         X, y, X_offset, y_offset, X_scale = self._preprocess_data(
             X,
diff --git a/sklearn/neighbors/_kde.py b/sklearn/neighbors/_kde.py
index 328a13371bafd..0ac0ea7226b90 100644
--- a/sklearn/neighbors/_kde.py
+++ b/sklearn/neighbors/_kde.py
@@ -191,9 +191,9 @@ def fit(self, X, y=None, sample_weight=None):
         X = self._validate_data(X, order="C", dtype=DTYPE)
 
         if sample_weight is not None:
-            sample_weight = _check_sample_weight(sample_weight, X, DTYPE)
-            if sample_weight.min() <= 0:
-                raise ValueError("sample_weight must have positive values")
+            sample_weight = _check_sample_weight(
+                sample_weight, X, DTYPE, only_non_negative=True
+            )
 
         kwargs = self.metric_params
         if kwargs is None:
diff --git a/sklearn/neighbors/tests/test_kde.py b/sklearn/neighbors/tests/test_kde.py
index 84f7623c8dbf1..d4fb775c44826 100644
--- a/sklearn/neighbors/tests/test_kde.py
+++ b/sklearn/neighbors/tests/test_kde.py
@@ -209,7 +209,7 @@ def test_sample_weight_invalid():
     data = np.reshape([1.0, 2.0, 3.0], (-1, 1))
 
     sample_weight = [0.1, -0.2, 0.3]
-    expected_err = "sample_weight must have positive values"
+    expected_err = "Negative values in data passed to `sample_weight`"
     with pytest.raises(ValueError, match=expected_err):
         kde.fit(data, sample_weight=sample_weight)
 
diff --git a/sklearn/utils/tests/test_validation.py b/sklearn/utils/tests/test_validation.py
index d1409d6129812..2cbbaac35a31b 100644
--- a/sklearn/utils/tests/test_validation.py
+++ b/sklearn/utils/tests/test_validation.py
@@ -52,8 +52,8 @@
     FLOAT_DTYPES,
     _get_feature_names,
     _check_feature_names_in,
+    _check_fit_params,
 )
-from sklearn.utils.validation import _check_fit_params
 from sklearn.base import BaseEstimator
 import sklearn
 
@@ -1253,6 +1253,14 @@ def test_check_sample_weight():
     sample_weight = _check_sample_weight(None, X, dtype=X.dtype)
     assert sample_weight.dtype == np.float64
 
+    # check negative weight when only_non_negative=True
+    X = np.ones((5, 2))
+    sample_weight = np.ones(_num_samples(X))
+    sample_weight[-1] = -10
+    err_msg = "Negative values in data passed to `sample_weight`"
+    with pytest.raises(ValueError, match=err_msg):
+        _check_sample_weight(sample_weight, X, only_non_negative=True)
+
 
 @pytest.mark.parametrize("toarray", [np.array, sp.csr_matrix, sp.csc_matrix])
 def test_allclose_dense_sparse_equals(toarray):
diff --git a/sklearn/utils/validation.py b/sklearn/utils/validation.py
index 87f957b931073..d45f246b233f8 100644
--- a/sklearn/utils/validation.py
+++ b/sklearn/utils/validation.py
@@ -1492,7 +1492,9 @@ def _check_psd_eigenvalues(lambdas, enable_warnings=False):
     return lambdas
 
 
-def _check_sample_weight(sample_weight, X, dtype=None, copy=False):
+def _check_sample_weight(
+    sample_weight, X, dtype=None, copy=False, only_non_negative=False
+):
     """Validate sample weights.
 
     Note that passing sample_weight=None will output an array of ones.
@@ -1503,17 +1505,22 @@ def _check_sample_weight(sample_weight, X, dtype=None, copy=False):
     Parameters
     ----------
     sample_weight : {ndarray, Number or None}, shape (n_samples,)
-       Input sample weights.
+        Input sample weights.
 
     X : {ndarray, list, sparse matrix}
         Input data.
 
+    only_non_negative : bool, default=False,
+        Whether or not the weights are expected to be non-negative.
+
+        .. versionadded:: 1.0
+
     dtype : dtype, default=None
-       dtype of the validated `sample_weight`.
-       If None, and the input `sample_weight` is an array, the dtype of the
-       input is preserved; otherwise an array with the default numpy dtype
-       is be allocated.  If `dtype` is not one of `float32`, `float64`,
-       `None`, the output will be of dtype `float64`.
+        dtype of the validated `sample_weight`.
+        If None, and the input `sample_weight` is an array, the dtype of the
+        input is preserved; otherwise an array with the default numpy dtype
+        is be allocated.  If `dtype` is not one of `float32`, `float64`,
+        `None`, the output will be of dtype `float64`.
 
     copy : bool, default=False
         If True, a copy of sample_weight will be created.
@@ -1521,7 +1528,7 @@ def _check_sample_weight(sample_weight, X, dtype=None, copy=False):
     Returns
     -------
     sample_weight : ndarray of shape (n_samples,)
-       Validated sample weight. It is guaranteed to be "C" contiguous.
+        Validated sample weight. It is guaranteed to be "C" contiguous.
     """
     n_samples = _num_samples(X)
 
@@ -1553,6 +1560,9 @@ def _check_sample_weight(sample_weight, X, dtype=None, copy=False):
                 )
             )
 
+    if only_non_negative:
+        check_non_negative(sample_weight, "`sample_weight`")
+
     return sample_weight