President-elect Donald Trump shuffled his transition team three days after his surprising victory, diluting the role of New Jersey Gov. Chris Christie 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 tasked with identifying candidates for 15 cabinet positions and about 1,000 top posts that must be confirmed by the Senate.

A former aide of Mr. Sessions, Stephen Miller, was named as national policy director of the transition, and several more of the senator’s former staffers are on a unit of the team that is dedicated to immigration policy, including Mr. Trump’s plan to build a wall along the Mexican border.

Mr. Christie will remain on the transition team’s executive committee as one of six vice chairmen, along with Mr. Sessions, former Republican presidential candidate Ben Carson, retired Lt. Gen. Michael Flynn, former House Speaker Newt Gingrich, and former New York Mayor Rudy Giuliani.

“President-elect Trump will bring about fundamental change in Washington, and these are the right people to make that happen,” Mr. Pence said.