The 24-year-old Ream links up with U.S. midfielder Stuart Holden and replaces England defender Gary Cahill, who switched to Chelsea earlier in Europe's January transfer window.
Ream signed a 3 1/2-year contract with the Premier League club. Neither Bolton nor Major League Soccer's Red Bulls disclosed the transfer fee.
Bolton manager Owen Coyle says Arsenal was among the clubs that tried to sign Ream before the start of the current English season.
Coyle says Ream is ''a player that year-on-year has progressed and got better - and he will continue to do that.''