The 24-year-old left-back, who has made the switch to London for an undisclosed fee, has been with the Robins all of his career, save two loan moves to Bath City and Plymouth Argyle.
"The left-back has signed a four-year-deal with Fulham, with a Club option to extend by a further year."
Bryan leaves Bristol after an 11-year stint during which he made 230 appearances and scored 20 goals. Since putting pen to paper, he has praised Fulham's philosophy, also expressing a desire to integrate quickly.
“Playing against Fulham the last couple of years, the style of play has really stood out to me and it will suit me," he remarked.
“The opportunity to play in the Premier League is one you can’t turn down as you may never get it again in your lifetime.
“I’m used to playing fast attacking football, so hopefully I can slot right in.”