The Norway international has been keen on a move to one of Europe's top leagues this summer, with his contract due to expire at the end of the year.
English and French clubs have been chasing Braaten, but it appears Bolton boss Sammy Lee has won the race for the 25-year-old.
"I don't know much about the place, but I do know some of the players and a little bit about the club," he told Dagbladet.
"It seems exciting. Definitely a step up."