diff --git a/sklearn/linear_model/_stochastic_gradient.py b/sklearn/linear_model/_stochastic_gradient.py
index 006bfc73da63e..ff6878d5e1686 100644
--- a/sklearn/linear_model/_stochastic_gradient.py
+++ b/sklearn/linear_model/_stochastic_gradient.py
@@ -158,14 +158,6 @@ def _more_validate_params(self, for_partial_fit=False):
         self._get_penalty_type(self.penalty)
         self._get_learning_rate_type(self.learning_rate)
 
-        # TODO(1.3): remove "log"
-        if self.loss == "log":
-            warnings.warn(
-                "The loss 'log' was deprecated in v1.1 and will be removed in version "
-                "1.3. Use `loss='log_loss'` which is equivalent.",
-                FutureWarning,
-            )
-
     def _get_loss_function(self, loss):
         """Get concrete ``LossFunction`` object for str ``loss``."""
         loss_ = self.loss_functions[loss]
@@ -501,13 +493,11 @@ def _get_plain_sgd_function(input_dtype):
 
 class BaseSGDClassifier(LinearClassifierMixin, BaseSGD, metaclass=ABCMeta):
 
-    # TODO(1.3): Remove "log""
     loss_functions = {
         "hinge": (Hinge, 1.0),
         "squared_hinge": (SquaredHinge, 1.0),
         "perceptron": (Hinge, 0.0),
         "log_loss": (Log,),
-        "log": (Log,),
         "modified_huber": (ModifiedHuber,),
         "squared_error": (SquaredLoss,),
         "huber": (Huber, DEFAULT_EPSILON),
@@ -517,7 +507,7 @@ class BaseSGDClassifier(LinearClassifierMixin, BaseSGD, metaclass=ABCMeta):
 
     _parameter_constraints: dict = {
         **BaseSGD._parameter_constraints,
-        "loss": [StrOptions(set(loss_functions), deprecated={"log"})],
+        "loss": [StrOptions(set(loss_functions))],
         "early_stopping": ["boolean"],
         "validation_fraction": [Interval(Real, 0, 1, closed="neither")],
         "n_iter_no_change": [Interval(Integral, 1, None, closed="left")],
@@ -950,7 +940,7 @@ class SGDClassifier(BaseSGDClassifier):
 
     Parameters
     ----------
-    loss : {'hinge', 'log_loss', 'log', 'modified_huber', 'squared_hinge',\
+    loss : {'hinge', 'log_loss', 'modified_huber', 'squared_hinge',\
         'perceptron', 'squared_error', 'huber', 'epsilon_insensitive',\
         'squared_epsilon_insensitive'}, default='hinge'
         The loss function to be used.
@@ -958,7 +948,7 @@ class SGDClassifier(BaseSGDClassifier):
         - 'hinge' gives a linear SVM.
         - 'log_loss' gives logistic regression, a probabilistic classifier.
         - 'modified_huber' is another smooth loss that brings tolerance to
-           outliers as well as probability estimates.
+          outliers as well as probability estimates.
         - 'squared_hinge' is like hinge but is quadratically penalized.
         - 'perceptron' is the linear loss used by the perceptron algorithm.
         - The other losses, 'squared_error', 'huber', 'epsilon_insensitive' and
@@ -969,10 +959,6 @@ class SGDClassifier(BaseSGDClassifier):
         More details about the losses formulas can be found in the
         :ref:`User Guide <sgd_mathematical_formulation>`.
 
-        .. deprecated:: 1.1
-            The loss 'log' was deprecated in v1.1 and will be removed
-            in version 1.3. Use `loss='log_loss'` which is equivalent.
-
     penalty : {'l2', 'l1', 'elasticnet', None}, default='l2'
         The penalty (aka regularization term) to be used. Defaults to 'l2'
         which is the standard regularizer for linear SVM models. 'l1' and
@@ -1249,8 +1235,7 @@ def __init__(
         )
 
     def _check_proba(self):
-        # TODO(1.3): Remove "log"
-        if self.loss not in ("log_loss", "log", "modified_huber"):
+        if self.loss not in ("log_loss", "modified_huber"):
             raise AttributeError(
                 "probability estimates are not available for loss=%r" % self.loss
             )
@@ -1295,8 +1280,7 @@ def predict_proba(self, X):
         """
         check_is_fitted(self)
 
-        # TODO(1.3): Remove "log"
-        if self.loss in ("log_loss", "log"):
+        if self.loss == "log_loss":
             return self._predict_proba_lr(X)
 
         elif self.loss == "modified_huber":
diff --git a/sklearn/linear_model/tests/test_sgd.py b/sklearn/linear_model/tests/test_sgd.py
index c5f0d4507227e..51c166869f174 100644
--- a/sklearn/linear_model/tests/test_sgd.py
+++ b/sklearn/linear_model/tests/test_sgd.py
@@ -716,8 +716,7 @@ def test_sgd_predict_proba_method_access(klass):
     # details.
     for loss in linear_model.SGDClassifier.loss_functions:
         clf = SGDClassifier(loss=loss)
-        # TODO(1.3): Remove "log"
-        if loss in ("log_loss", "log", "modified_huber"):
+        if loss in ("log_loss", "modified_huber"):
             assert hasattr(clf, "predict_proba")
             assert hasattr(clf, "predict_log_proba")
         else:
@@ -2060,29 +2059,6 @@ def test_SGDClassifier_fit_for_all_backends(backend):
     assert_array_almost_equal(clf_sequential.coef_, clf_parallel.coef_)
 
 
-# TODO(1.3): Remove
-@pytest.mark.parametrize(
-    "old_loss, new_loss, Estimator",
-    [
-        ("log", "log_loss", linear_model.SGDClassifier),
-    ],
-)
-def test_loss_deprecated(old_loss, new_loss, Estimator):
-
-    # Note: class BaseSGD calls self._validate_params() in __init__, therefore
-    # even instantiation of class raises FutureWarning for deprecated losses.
-    with pytest.warns(FutureWarning, match=f"The loss '{old_loss}' was deprecated"):
-        est1 = Estimator(loss=old_loss, random_state=0)
-        est1.fit(X, Y)
-
-    est2 = Estimator(loss=new_loss, random_state=0)
-    est2.fit(X, Y)
-    if hasattr(est1, "predict_proba"):
-        assert_allclose(est1.predict_proba(X), est2.predict_proba(X))
-    else:
-        assert_allclose(est1.predict(X), est2.predict(X))
-
-
 @pytest.mark.parametrize(
     "Estimator", [linear_model.SGDClassifier, linear_model.SGDRegressor]
 )