diff --git a/doc/whats_new.rst b/doc/whats_new.rst
index a434ed82a11b8..cc481740c96f7 100644
--- a/doc/whats_new.rst
+++ b/doc/whats_new.rst
@@ -97,6 +97,10 @@ Bug fixes
      in R (lars library). :issue:`7849` by `Jair Montoya Martinez`_
 
 
+   - Fix a bug regarding fitting :class:`sklearn.cluster.KMeans` with a
+     sparse array X and initial centroids, where X's means were unnecessarily
+     being subtracted from the centroids. :issue:`7872` by `Josh Karnofsky <https://github.com/jkarno>`_.
+
 .. _changes_0_18_1:
 
 Version 0.18.1
diff --git a/sklearn/cluster/k_means_.py b/sklearn/cluster/k_means_.py
index bd48a1c36224a..f33b3f65b714e 100644
--- a/sklearn/cluster/k_means_.py
+++ b/sklearn/cluster/k_means_.py
@@ -298,18 +298,11 @@ def k_means(X, n_clusters, init='k-means++', precompute_distances='auto',
                          ", but a value of %r was passed" %
                          precompute_distances)
 
-    # subtract of mean of x for more accurate distance computations
-    if not sp.issparse(X) or hasattr(init, '__array__'):
-        X_mean = X.mean(axis=0)
-    if not sp.issparse(X):
-        # The copy was already done above
-        X -= X_mean
-
+    # Validate init array
     if hasattr(init, '__array__'):
         init = check_array(init, dtype=X.dtype.type, copy=True)
         _validate_center_shape(X, n_clusters, init)
 
-        init -= X_mean
         if n_init != 1:
             warnings.warn(
                 'Explicit initial center position passed: '
@@ -317,6 +310,15 @@ def k_means(X, n_clusters, init='k-means++', precompute_distances='auto',
                 % n_init, RuntimeWarning, stacklevel=2)
             n_init = 1
 
+    # subtract of mean of x for more accurate distance computations
+    if not sp.issparse(X):
+        X_mean = X.mean(axis=0)
+        # The copy was already done above
+        X -= X_mean
+
+        if hasattr(init, '__array__'):
+            init -= X_mean
+
     # precompute squared norms of data points
     x_squared_norms = row_norms(X, squared=True)
 
diff --git a/sklearn/cluster/tests/test_k_means.py b/sklearn/cluster/tests/test_k_means.py
index 4b23ab9cc1677..31307e55801a5 100644
--- a/sklearn/cluster/tests/test_k_means.py
+++ b/sklearn/cluster/tests/test_k_means.py
@@ -812,7 +812,7 @@ def test_float_precision():
                                       decimal=4)
 
 
-def test_KMeans_init_centers():
+def test_k_means_init_centers():
     # This test is used to check KMeans won't mutate the user provided input
     # array silently even if input data and init centers have the same type
     X_small = np.array([[1.1, 1.1], [-7.5, -7.5], [-1.1, -1.1], [7.5, 7.5]])
@@ -824,3 +824,47 @@ def test_KMeans_init_centers():
         km = KMeans(init=init_centers_test, n_clusters=3, n_init=1)
         km.fit(X_test)
         assert_equal(False, np.may_share_memory(km.cluster_centers_, init_centers))
+
+
+def test_sparse_k_means_init_centers():
+    from sklearn.datasets import load_iris
+
+    iris = load_iris()
+    X = iris.data
+
+    # Get a local optimum
+    centers = KMeans(n_clusters=3).fit(X).cluster_centers_
+
+    # Fit starting from a local optimum shouldn't change the solution
+    np.testing.assert_allclose(
+        centers,
+        KMeans(n_clusters=3,
+               init=centers,
+               n_init=1).fit(X).cluster_centers_
+    )
+
+    # The same should be true when X is sparse
+    X_sparse = sp.csr_matrix(X)
+    np.testing.assert_allclose(
+        centers,
+        KMeans(n_clusters=3,
+               init=centers,
+               n_init=1).fit(X_sparse).cluster_centers_
+    )
+
+
+def test_sparse_validate_centers():
+    from sklearn.datasets import load_iris
+
+    iris = load_iris()
+    X = iris.data
+
+    # Get a local optimum
+    centers = KMeans(n_clusters=4).fit(X).cluster_centers_
+
+    # Test that a ValueError is raised for validate_center_shape
+    classifier = KMeans(n_clusters=3, init=centers, n_init=1)
+
+    msg = "The shape of the initial centers \(\(4L?, 4L?\)\) " \
+          "does not match the number of clusters 3"
+    assert_raises_regex(ValueError, msg, classifier.fit, X)