Adams, 23, joins for an undisclosed fee thought to be around £20million, with the Whites moving to wrap up a deal for the American after selling Kalvin Phillips to Manchester City for £42million.
Adams - captain of the US national team - is well known to Leeds boss and fellow countryman Jesse Marsch.
Marsch managed him during their time together at both New York Red Bulls and RB Leipzig where he made 103 appearances for the club.
While Adams is a central midfielder, he can also play at right-back, where has has featured for the US.
"I am super excited," Adams told LUTV.
"Walking in for the first time, meeting people today at the training ground and coming to the stadium, which is empty now, but I can't wait to play in front of a full crowd!
"I know a little bit about the club. I watched the documentary which is quite popular and I was able to learn a lot of important things about the club.
"The one thing for me is the passion of the fans and the city, what it requires to be a Leeds United player.
"So far what I have heard is that it's electric here. Talking to my friends who have played in the Premier League, they say it's one of the best atmospheres they have ever played in.
"Now to have those fans supporting me, it's going to be something special."
Feyenoord winger Luis Sinisterra is also set to arrive as a potential replacement for Raphinha, who is wanted by Barcelona and Chelsea.
The 23-year-old Colombia international is set to cost around £20million too.
Sinisterra, meanwhile, has been at Feyenoord for the past four years and had his best season in 2021/22.
The exciting winger scored 23 goals and registered 14 assists in all competitions.
It is likely he will be a direct replacement for Raphinha.
Arsenal had previously seen two bids rejected for the 25-year-old, and despite Leeds accepting a £60m offer for their star from Chelsea, the player is understood to be holding out for a move to Barcelona.