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|Fabri played six matches as Besiktas reached the Champions League last 16 last season. (AFP/BULENT KILIC)|
London side Fulham also hold an option to keep the 30-year-old at Craven Cottage for an additional 12 months.
"I'm delighted to be at an historic club like Fulham, the oldest club in London. I'm very happy to have the opportunity to be in the Premier League with Fulham," Fabri told the club's website.
"Everything is very positive for me and I want to take the opportunity to make the most of this goal of being in the Premier League," he added.
Fabri started his career with Deportivo La Coruna, where he worked with Jose Sambade Carreira, now Fulham's goalkeeping coach, and played for several other Spanish clubs in Real Valladolid, Recreativo de Huelva, and Real Betis.
He moved to Turkey in 2016 and went onto play Champions League and Europa League football for Besiktas.
Fabri was also voted the best goalkeeper in the Super Lig for the last two years.
"He is a tremendous player that we've targeted for some time," said Fulham vice-chairman Tony Khan.
"His scouting profile and his data profile are both strong, and he has exceptional career credentials including Champions League experience, plus he has worked well with our first-team goalkeeping coach Jose Sambade Carreira in the past, so we expect his addition will make us a more complete and competitive football club."
Fabri is Fulham's third new signing since their promotion from the second-tier Championship after both Maxime Le Marchand and Jean Michael Seri joined from French side Nice.