Fulham will now pay Eintracht Frankfurt €22 million (£19m) for the Swedish midfielder after German outlet Kicker reported the buy clause required only a single competitive appearance, which Larsson made when he came on as a 79th-minute substitute for Oscar Bobb during Saturday's 3-2 defeat.
The 22-year-old joined Fulham on deadline day on a season-long loan with a mandatory purchase option, having spent three years at Eintracht Frankfurt after his move from Malmö FF in the summer of 2023.
The move capped a fast-moving deadline-day saga. Larsson had travelled to England to discuss a possible £18-20 million switch, with Crystal Palace also in the running before he agreed personal terms with Fulham and completed his medical.
Frankfurt's board member for sport, Markus Krösche, paid tribute to the midfielder on the club's departure: "Hugo Larsson has been one of our key first-team players over the past three years and has played a big part in our success.
"We'd like to thank Hugo for his commitment in an Eintracht shirt and wish him all the best for his future career."
Larsson developed into an important fixture in Frankfurt's midfield, making 119 competitive appearances and contributing ten goals and seven assists across his time in Germany, often operating as part of an asymmetric double pivot alongside Ellyes Skhiri. He made 61 appearances for Malmö before his move abroad, scoring three goals and adding four assists.
The Sweden international has earned 12 senior caps but was left out of his country's squad for this summer's World Cup. His arrival came as part of a busy deadline day for Fulham, who also completed a permanent deal for Real Madrid's Manuel Angel on the same day, but the club have made a miserable start to the new Premier League season, losing all three of their opening fixtures.