Ghana international Boateng, 30, has signed a one-year contract with the Cottagers with the option of a further year.
The former Getafe, Cologne and Beitar Jerusalem star has been a long-term target of Fulham manager Martin Jol and a dispute with Ukrainian club Dnipro prevented him making the move to Craven Cottage earlier this season.
Boateng told the club's official website: "I'm very happy that I have signed and I want to thank the chairman, the manager and the board at Fulham Football Club.
"I've been working hard to come here and I'll do my best for the club.
"It's been a long road for me but now I'm here I'm so happy and I can't wait to start and give everything I have."
Venezuela centre-back Amorebieta has signed a four-year deal with Fulham after eight seasons in La Liga with Athletic Bilbao.
The 28-year-old told the club's website: "I'm delighted to have signed a four-year deal with Fulham and I'm looking forward to competing in the Barclays Premier League next season.
"I'm impressed with the talent already at the club and I look forward to meeting the players for pre-season training in July."
The Londoners beat off reported interest from Arsenal, Everton and Zenit St Petersburg to sign Amorebieta, who has made more than 250 appearances for Bilbao.