Eintracht Frankfurt's asking price was met when the buy-option clause in Larsson's loan agreement was triggered by his first competitive appearance for the west London club earlier this month, converting the move into a permanent €22 million transfer.
The structure means Malmö FF, who sold Larsson to Frankfurt for an initial fee in 2023, are now due a sell-on percentage on top of what they received three years ago, having negotiated a resale clause into the original deal.
"Frankfurt were quite generous, and I'm grateful for that. It was very straightforward for the option to be met," Larsson told Fotbollskanalen.
The 22-year-old, who made 119 appearances and scored ten goals across three years in Germany, says the move itself has been one of the highlights of an eventful summer.
"One of the things that made the summer good was my move. Moving to the best league in the world and an incredible club like Fulham - it's been intense, but it's fun and I'm settling in really well," he said.
At Craven Cottage he is working under Álvaro Arbeloa, the former Real Madrid defender who took the Fulham job over the summer.
"He's good, tactically knowledgeable and has a good feel for handling the group. We all enjoy working with him - results haven't gone our way yet, but I think everyone at the club, and around it, can see we're playing good football. I think it's a matter of time before results come," Larsson said.
The permanent transfer has coincided with a shift in his international fortunes. Larsson was a notable absentee from Graham Potter's World Cup squad this summer, a decision that provoked strong reaction in Sweden given his standing as one of the country's most talked-about midfielders.
He was left out again when Potter named his initial squad for this month's Nations League fixtures, but has now been called into the group after Mattias Svanberg withdrew through injury.
Larsson had previously stayed largely quiet on the World Cup snub, but has now opened up on how he dealt with it.
"Of course I wanted to be involved, and having been part of the whole journey, I wanted it even more. But at the end of the day, that wasn't the decision that was made. And I just had to accept it," he told SVT Sport.
He also pointed to his relocation to England as a factor that softened the disappointment.
"I wasn't involved in the World Cup either, so... of course you always want to be involved here, but if I'm completely honest, I had so much going on with the move that in a way I thought, well, I can sort that out - life isn't just football," he said, before adding: "But of course I wanted to be involved, and I was as happy as could be when he [Graham Potter] called."
Sweden were promoted to League B after winning their League C group last season under then-manager Jon Dahl Tomasson, and Potter's side open their new campaign at home to Romania on Friday.