The 24-year-old has signed a three-and-a-half year contract with Bolton and joins the club for an undisclosed fee.
Ream spent a week training with Bolton at the end of last year.
"First and foremost we are absolutely delighted to secure Tim's services," said Bolton manager Owen Coyle.
"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."