WASHINGTON—Republican senators chose John Thune of South Dakota as their first new leader in nearly two decades, opting for continuity over calls for radical change heading into populist President-elect Donald Trump’s second term in the White House.

Sen. John Thune of South Dakota is one of the most powerful people in Washington that folks outside D.C. have never heard of.

Many Republican senators were stunned that Representative Matt Gaetz, Republican of Florida, had been chosen as the nominee, and expressed skepticism that he could secure enough votes for confirmation.