Francona won easily to become the 15th manager to win the award more than once.
Francona won easily, getting 22 of the 30 first-place votes and 128 total voting points in voting by the members of the Baseball Writers Association of America.
Francona, who also won the award with the Indians in 2013, is the 15th manager to win the award more than once.
Roberts received 16 of the 30 first-place votes and had 108 total voting points.
Roberts led the Dodgers to a 91-71 record and an NL West title in his first year as a manager.
He accomplished that even though 28 Dodgers players were sent to the injured list in 2016. That included ace pitcher Clayton Kershaw, who missed two months with a back problem.