President-elect Donald Trump shuffled his transition team three days after his surprising victory, diluting the while increasing the influence of Vice President-elect Mike Pence and Alabama Sen. Jeff Sessions, one of Washington’s most vocal critics of illegal immigration.

Mr. Christie was removed on Friday as transition chairman, a position now filled by Mr. Pence, the transition team said. Mr. Sessions’ chief of staff, Rick Dearborn, was elevated to the role of transition director, overseeing the day-to-day work of the team...