France Under-20 striker Moussa Dembele has signed a four-year contract with Scottish champions Celtic, who have allowed forward Stefan Scepovic to sign for Getafe on a permanent basis.
Dembele was out of contract at Fulham, who will be due a development fee.
Scepovic, 26, who was contracted until 2018, has been sold to Getafe after spending last season on loan there.
Dembele, 19, scored 17 goals for Fulham in 46 games last season and is Brendan Rodgers' first signing at Celtic.
He joined Fulham from Paris St-Germain as a 16-year-old and made his debut for the London club in a Premier League game against West Ham United in November 2013.
His goals helped Fulham avoid relegation last season as the London club finished 20th in the English Championship, two places above the drop zone.
Dembele told Celtic's website: "To be the first signing of Brendan Rodgers is unreal for me.
"He told me that Celtic is a good team for me. I will have game time. I obviously have to show I can stay in the team.
"I think it's a good way for me to progress. It's unbelievable for me to play for a massive club like this."
Serb Scepovic played only one game for the Glasgow club last season before moving to Spain.
He scored six goals in 25 games in an underwhelming first season at Celtic Park after arriving from Sporting Gijon for £2.3m on transfer deadline day in August 2014.
Scepovic, who has also played for Beograd, Sampdoria, Club Brugge, Hapoel Acre, Partizan Belgrade and Ashdod, scored six times in 34 appearances while on loan in Spain.
Getafe, who were relegated from La Liga to the Segunda Division, say Scepovic has signed a four-year contract.
He becomes the fourth striker to exit Celtic Park since Rodgers succeeded Ronny Deila as manager at the end of May.
Anthony Stokes joined Blackburn Rovers after the Irishman was not offered a new contract, while former Turkey forward Colin Kazim-Richards was transferred to Brazilian club Curitiba and former England player Carlton Cole's contract was terminated.