The team includes at Treasury, Steven Mnuchin, a former Goldman Sachs partner turned hedge fund manager who has spoken favorably of infrastructure spending that Mr. Mulvaney has opposed; a commerce secretary nominee, Wilbur Ross, known for the billions of dollars he has earned through international investing; and a National Economic Council director, Gary Cohn, who as president of Goldman Sachs has channeled tens of thousands of dollars in campaign contributions to Democrats as well as Republicans.

Mr. Mulvaney, who did not respond to emails seeking comment, has cut an influential swath among House conservatives since he was elected in the Tea Party wave of 2010, when he defeated a longtime representative, John Spratt, a Democrat. He won by characterizing his opponent as a big-spending liberal, unconcerned about fiscal prudence, even though as chairman of the House Budget Committee, Mr. Spratt was among his party’s leading deficit hawks.

Since then, Mr. Mulvaney has perpetually rejected short-term spending agreements and questioned the government’s need to increase its statutory borrowing limits to avoid default. He has repeatedly opposed some of his own party’s budget proposals, and quickly established himself as one of the most outspoken members of that 2010 class of Republicans. By 2013, at the start of his second term, he declined to support Mr. Boehner’s re-election as speaker, abstaining from the vote in protest.

At the same time, unlike some members of the caucus, Mr. Mulvaney, 49, has also supported Paul D. Ryan, Mr. Boehner’s successor as speaker, and has served as a quiet back channel between Mr. Ryan and conservative members. Impish and sometimes short-tempered, Mr. Mulvaney seemed to chafe at serving in the shadow of Mr. Gowdy and Mr. Scott, who are best friends and shining stars in their party and home state.

Mr. Mulvaney has now found a political home where he can stand out.

He has often served as an articulate spokesman for the right’s spending and social-policy positions, far more than many other Freedom Caucus members, who often seem more concerned with self-promotion than policy persuasion.