Castagne has signed a four-year contract at Craven Cottage with the option for a further year.
The 27-year-old Belgium international has cost Marco Silva's side £13m after spending three years at the King Power Stadium.
Castagne joined the Foxes from Serie A side Atalanta in the summer of 2020 and the versatile full back chipped in with five goals in 112 appearances for Leicester, winning the FA Cup in 2021.
He made 37 appearances as Leicester suffered relegation to the Championship last season.
After his arrival was confirmed, Castagne told FFCtv: 'I feel very good. 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 vice-chairman and director of football operations 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!'
Castagne could make his debut against Manchester City this weekend.
