The Cottagers have refrained from disclosing the finances involved in wrapping up a deal, but Castagne is believed to have cost around £15 million.
The 27-year-old has penned a four-year deal that will keep him associated with the Craven Cottage club until 2027, with a club option for a further 12 months.
The experienced Belgium international is naturally a right-back but is adaptable enough to also feature on the opposite side of the defence.
Castagne’s versatility will come in handy for Marco Silva’s side, and he becomes their fourth signing of the transfer window, following the arrivals of Raul Jiminez, Calvin Bassey and Adama Traore.
“I feel very good,” Castagne said. “It’s been a long transfer window, but finally, I’m here, and I’m happy to be here.
“It’s a big relief. I’ve talked to the Manager, and I just can’t wait to start training and playing.”
Fulham chief Tony Khan added: “I’m excited to welcome Timothy Castagne to Fulham.
“He’s a versatile and very talented defender with great experience in the Premier League and international competition for Belgium.
“I’m pleased that Timothy has committed to a four-year contract with us, and we believe that he’ll be an excellent addition to Marco’s squad.”
Fulham are still looking to do some business before the transfer window closes, as a striker remains a priority for Silva.
The Cottagers have lost Aleksandar Mitrovic in a club-record sale to the Saudi Pro League, and they are eager to sign a capable replacement before Friday’s deadline.
Fulham have also had a £21m bid rejected for Flamengo striker Pedro. The Brazilian outfit are reluctant to sell, but the Cottagers are expected to return with an improved proposal.
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