diff --git a/bigquery/storage_client.go b/bigquery/storage_client.go
index a1fae7674b7e..8c48ed308ca1 100644
--- a/bigquery/storage_client.go
+++ b/bigquery/storage_client.go
@@ -107,15 +107,8 @@ func (c *readClient) sessionForTable(ctx context.Context, table *Table, rsProjec
 		settings.maxStreamCount = 1
 	}
 
-	// configure where the read session is created
-	readSessionProjectID := table.ProjectID
-	if useClientProject {
-		readSessionProjectID = c.projectID
-	}
-
 	rs := &readSession{
 		ctx:                   ctx,
-		readSessionProjectID:  readSessionProjectID,
 		table:                 table,
 		tableID:               tableID,
 		projectID:             rsProjectID,
diff --git a/bigquery/storage_integration_test.go b/bigquery/storage_integration_test.go
index 492561c8a488..d1fac66add5b 100644
--- a/bigquery/storage_integration_test.go
+++ b/bigquery/storage_integration_test.go
@@ -112,6 +112,15 @@ func TestIntegration_StorageReadClientProject(t *testing.T) {
 	if !strings.HasPrefix(session.bqSession.Name, expectedPrefix) {
 		t.Fatalf("expected read session to have prefix %q: but found %s:", expectedPrefix, session.bqSession.Name)
 	}
+
+	it = table.Read(ctx, WithReadSessionProject("bigquery-public-data"))
+	_, err = countIteratorRows(it)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if it.IsAccelerated() {
+		t.Fatal("expected storage api to not be used")
+	}
 }
 
 func TestIntegration_StorageReadFromSources(t *testing.T) {
diff --git a/bigquery/table.go b/bigquery/table.go
index 012d58aba790..56058f46daf5 100644
--- a/bigquery/table.go
+++ b/bigquery/table.go
@@ -968,17 +968,16 @@ func (t *Table) Delete(ctx context.Context) (err error) {
 }
 
 type tableReadOption struct {
-	useClientProject bool
+	readSessionProject string
 }
 
 // TableReadOption allows requests to alter the behavior of reading from a table.
 type TableReadOption func(*tableReadOption)
 
-// WithClientProject allows the read session to be created from the client project
-// when reading from the table, instead of the table's project.
-func WithClientProject() TableReadOption {
+// WithReadSessionProject allows to create the read session with the specified project that has the necessary permissions to do so.
+func WithReadSessionProject(project string) TableReadOption {
 	return func(tro *tableReadOption) {
-		tro.useClientProject = true
+		tro.readSessionProject = project
 	}
 }
 
@@ -988,13 +987,17 @@ func (t *Table) Read(ctx context.Context, opts ...TableReadOption) *RowIterator
 }
 
 func (t *Table) read(ctx context.Context, pf pageFetcher, opts ...TableReadOption) *RowIterator {
-	tro := &tableReadOption{useClientProject: false}
+	tro := &tableReadOption{}
 	for _, o := range opts {
 		o(tro)
 	}
 
+	if tro.readSessionProject == "" {
+		tro.readSessionProject = t.c.projectID
+	}
+
 	if t.c.isStorageReadAvailable() {
-		it, err := newStorageRowIteratorFromTable(ctx, t, false, tro.useClientProject)
+		it, err := newStorageRowIteratorFromTable(ctx, t, tro.readSessionProject, false)
 		if err == nil {
 			return it
 		}