When Malaysia’s then-Prime Minister Mahathir Mohamad popularized the catchphrase “Malaysia Boleh!”—Malaysia Can!—in the 1990s, it was meant to showcase the economic achievements of an authoritarian state. Now that Dr. Mahathir, 92, is returning to power at the head of a disparate “Alliance of Hope” of pro-democracy forces, including former foes he once put behind bars, “Malaysia Boleh” has acquired a different meaning.

“Malaysia’s message is that democratic transitions are possible,” said Tony Pua, a lawmaker with the new...