The four were part of a group known as the "Hong Kong 47," and were rounded up for taking part in an unofficial primary poll in 2020 that drew more than 600,000 people.
John Lee, who has spent most of his civil service career in the police and overseeing security matters, has much less policy-making experience than previous chief executives.
Demands for expanded democracy in the semi-autonomous territory inspired protest movements that were largely ignored by Beijing and crushed by security forces.
The activists were intercepted as they tried to flee to Taiwan by speedboat. Two people accused of organizing the trip got the stiffest penalties, two and three years in prison.