Republicans’ decisive Senate takeover has transformed what was once a body full of traditionalists who viewed Donald J. Trump with skepticism and even some disdain into a compliant and loyal chamber full of allies ready to advance his agenda.

Gone is the uncertainty and unease that met Mr. Trump from some G.O.P. quarters on Capitol Hill eight years ago, when his victory was wholly unexpected, his policy agenda largely unknown and leading Republicans were willing to challenge him. The incoming president and nearly every senator in the new majority of at least 52 Republicans now share almost identical goals on big issues such as taxes, immigration, energy production and domestic social policy.

As they celebrated their victories on Wednesday and the party pressed to hold onto its House majority, Republicans made clear that the Senate, at least, is Mr. Trump’s to command.

“I think the Senate is going to give great deference to a president that just won a stunning, what I think is an Electoral College landslide, when all is said and done,” Senator Marco Rubio, Republican of Florida and a one-time Trump rival, said on CNN.

Republicans are well aware that they owe their new numbers directly to Mr. Trump, who provided the political momentum to pull some of their winners over the finish line in red states where veteran incumbent Democrats were defeated in tough, very expensive races in Ohio and Montana. They included two candidates who aligned themselves closely with Mr. Trump’s policies: Senators-elect Tim Sheehy of Montana, a wealthy businessman and former Navy SEAL. and Bernie Moreno of Ohio, a former luxury car dealer

Senate leaders were holding out hope that they could push their numbers beyond 52 and perhaps pick up another seat or two. The size of the majority is crucial, since larger numbers give Republicans more cushion in the event of possible policy disagreements or defections on nominees.