The United States international joins the Cottagers for an undisclosed fee, leaving the Macron Stadium after two-and-a-half years.
Ream, 27, has penned a deal to keep him at Craven Cottage until 2019, with the Whites retaining an option to extend his stay by a further year.
The deal was prolonged due to delays in Ream obtaining a work permit and once the process was completed, he told Fulham’s official website: “I’m more than pleased to be here.
“It’s been a long time coming now, over the past week and a half it’s gone back and forth so I’m glad it’s finally sorted.
“The biggest thing was the history, walking into the training ground and feeling the vibe around the club and the success that previous American players have had here.”
Ream, who has 13 international caps, joined Bolton from New York Red Bulls, going on to make 126 appearances across the Premier League, Championship, FA Cup and Capital One Cup and he was twice voted Supporters’ Player of the Season.