The deal for the 24-year-old England international was worth a reported club-record $69 million, including add-ons.
Fulham play Manchester United at Old Trafford on August 16 in the first match of the English Premier League season.
Smith Rowe joined Arsenal's academy at the age of 10 and progressed through the ranks to make 115 senior appearances for the Gunners in all competitions.
"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," he said.
Meanwhile Newcastle have opened talks with Crystal Palace over highly-rated England defender Marc Guehi, the PA news agency have reported.
It is understood Newcastle have registered their interest in the last week and held initial talks over a player who is valued at in excess of $118 million.
Guehi, who made 29 appearances in all competitions for the Eagles last season, started six of England's seven games at the Euro 2024 finals and only missed the seventh, the quarter-final victory over Switzerland, through suspension.
The central defender, whose current deal at Selhurst Park is due to expire in the summer of 2026, significantly enhanced his reputation in Germany and it is unlikely that Newcastle will be his only suitors.
Leeds winger Crysencio Summerville has passed a medical ahead of his switch to West Ham.
Reports in England suggest the 22-year-old Dutchman, who was the Championship player of the year last season, is expected to complete the formalities of the move over the weekend.
At around $50 million, Summerville will become West Ham's fourth signing of the summer. He scored 21 goals in all competitions for Leeds last season and was third-highest scorer in the Championship with 19.
Andrey Santos, Chelsea Brazilian midfielder, has rejoined Strasbourg on a season-long loan after making 11 appearances for the Ligue 1 side during the second half of last season.
The 20-year-old, who is yet to feature in the first team at Stamford Bridge since signing from Vasco da Gama in January 2023, had an unsuccessful spell at Nottingham Forest during the 2023-24 season, cut short after he played just twice in five months.
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