Bryan broke the deadlock in the 105th minute from a free kick from 35 metres out.
With Brentford goalkeeper David Raya and the rest of the defenders and attackersexpecting a cross, Bryan instead fired into the space at Raya’s near post.
Bryan added his second in the 117th minute after a slick exchange of passes with substitute Aleksandar Mitrovic.
Though Henrik Dalsgaard halved the deficit soon after, Thomas Frank's team could not find the equaliser to force a penalty shoot-out.
“What makes me so happy is that I see a group of players who only a year ago were struggling psychologically and didn't have a mindset or mentality,” Fulham boss Scott Parker told Sky Sports.
"I've driven this team every single day and what makes me proud is I that I’ve stood on the touchline and have seen a team that represents what I've been saying over the last 12 months."
Financial analysts estimate Fulham will earn around 140 million euros from their return to the Premier League after their relegation to the second tier Championship at the end of the 2018/19 season.
Slump
Brentford, who had been aiming for a place in the top flight for the first time in 73 years, were on the brink of gaining one of the two automatic promotion places last month before successive defeats against struggling Stoke City and Barnsley torpedoed their drive.
They finished third, two points behind second-placed West Bromwich Albion as Leeds United claimed the division.
"Of course it's tough when you lose a final like this in a very tight game but I'm extremely proud of my players," said Frank.
"We have gone from a mid-table club to a team who, in the league table, was the third-best team. We are very fine margins away from the Premier League, which is an incredible achievement from us."
