Tesla Inc. named a pair of new independent directors—including Oracle Corp. Chairman and tech-industry luminary Larry Ellison—to a board that has been under fire for its oversight of Chief Executive Elon Musk.

Tesla said Mr. Ellison, who has been a public booster of the electric-car maker, and Kathleen Wilson-Thompson, the global head of human resources for Walgreens Boots Alliance Inc., joined its board on Thursday.

Their...