While the Cottagers have not disclosed the total fee for the 24-year-old, it is understood the deal could rise to £34m with add-ons.
Smith Rowe, who joined Arsenal as a 10-year-old, made his senior debut for the Gunners at the age of 18 and made 80 Premier League appearances for the club, scoring 12 times.
He has three England caps, although his last came in March 2022.
“I’m finally here, so I’m really happy for me and my family – it’s a good moment,” said Smith Rowe.
“I’m really excited, I just wanted to get here as quickly as possible so I could get going with my team-mates.
“Listening to the project, speaking to the manager [Marco Silva], and seeing what players we have here already, I think it’s an exciting project for me, and definitely the perfect step for my career going forward.”
Fulham have also signed Ryan Sessegnon on a two-year deal after his contract expired at Tottenham and Cottagers vice-chairman Tony Khan said he was “thrilled” with the arrival of Smith Rowe.
“We’re very excited to sign such a talented young player, and we look forward to Emile joining the squad in Portugal as we continue to prepare for the new season ahead,” said Khan.
Fulham are also trying to sign Manchester United midfielder Scott McTominay, having made a second bid, believed to be worth £20m, for the 27-year-old Scotland international.