The deal reunites Garcia with Fulham head coach Alvaro Arbeloa, who coached him during his time in Real Madrid's youth system before taking charge of the London club in early July.
Spanish reports have said the transfer was worth around 40 million euros, while Real Madrid have kept a 30 per cent sell-on clause as part of the agreement.
Garcia enjoyed the best season of his career last term, scoring eight goals for Real Madrid, including six in La Liga. One of his standout performances came in January when he scored a hat-trick against Real Betis.
Speaking to FFCtv after completing the move, Garcia said he was eager to begin the next chapter of his career.
"I'm very grateful and very happy to be here. I have to thank the board and Arbeloa for the trust they've put in me, and I'm very, very excited to start."
Fulham vice-chairman Tony Khan believes the club have signed one of Spain's brightest young forwards.
"Gonzalo is a very talented young striker, and he is excited to come to Fulham and play in the Premier League," Khan said.
Garcia is not the only player to follow Arbeloa from Madrid to west London. Attacking midfielder Cesar Palacios has also joined Fulham after breaking into the Real Madrid first team under the Spanish coach.
Meanwhile, Real Madrid are continuing to reshape their squad after failing to win a major trophy in each of the last two seasons. Jose Mourinho has taken over as head coach following Arbeloa's departure.
Garcia could make his first appearance for Fulham when they face Crystal Palace in a pre-season friendly at Craven Cottage on 7 August.
Manchester City midfielder Nico Gonzalez believes the players are making good progress under new head coach Enzo Maresca, although he admitted it will take time before the squad fully understands everything the Italian wants from them.
Marc-Andre ter Stegen has completed a season-long loan move from Barcelona to Ajax, bringing an end to weeks of speculation over the experienced goalkeeper's future.
Jorrel Hato believes Chelsea can achieve something special this season under new head coach Xabi Alonso as he looks to build on an encouraging first year at Stamford Bridge.
Barcelona coach Hansi Flick has said the club still need to strengthen their attacking options before the new season, with uncertainty surrounding Ferran Torres and after the departures of Robert Lewandowski and Marcus Rashford.
