The 24-year-old, who has penned a three-and-a-half-year deal, has long been linked with a move to the Trotters and spent a week training with the club last year.
Ream's arrival, which is subject to international clearance and immigration formalities, comes just over a week after England international Gary Cahill sealed his move to Chelsea.
Bolton boss Owen Coyle said: "First and foremost we are absolutely delighted to secure Tim's services. He is a US international, a player that year on year has progressed and got better, and he will continue to do that.
"He was trailed by a number of clubs, including West Brom and also Arsenal, who tried to sign him in the summer, so it is great that he sees his future here.
"Tim is everything that we want in the players we are bringing to the club when we spend in the transfer market.
"He is young, has a tremendous attitude and a winning mentality. I know he will fit in well with the rest of the squad here at Bolton."
Ream has been a virtual ever-present for the Red Bulls over the last two Major League Soccer seasons and has played seven times for the USA team, making his full debut against South Africa in November 2010.