The Venezuela international has already agreed a Bosman deal with the Cottagers, and the transfer should be officially announced in the coming days.
Amorebieta was in London during the Easter holidays to get a feel for the club and his new surroundings, report AS.
The highly rated defender has rejected a new contract offer from Athletic Bilbao and he made it clear that he would like to join a Premier League side.
With Arsenal expressing interest, he was probably hoping to sign for a top 4 side, but ultimately opted to accept an offer from Fulham.
The 28-year-old has spent his entire career up to date at San Mames, making 194 La Liga appearances for los Leones.
He largely impressed during club’s Europa League and Copa del Rey runs last term, but has lost his starting place this season.