J.Crew Group Inc. said its longtime leader Mickey Drexler will step aside as chief executive and hand over those duties to an outsider, as the seller of preppy clothes struggles with a prolonged sales slump and hefty debt load.

The closely held company named James Brett, president of West Elm, as CEO starting next month. Mr. Drexler, who is 72 years old and has been CEO since 2003, will continue to serve as board chairman.

The...