The 43-year-old succeeds Marco Silva, who departed Craven Cottage after five years in charge to join Portuguese side Benfica.
Arbeloa, who played for Liverpool and West Ham in England, led Real Madrid for the last 28 games of last season as they finished second in La Liga and were knocked out of the Champions League quarter-finals by Bayern Munich.
He left the Spanish giants at the end of 2025/26 and was replaced by Jose Mourinho, who is now in his second spell at the Bernabéu.
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Alvaro Arbeloa, pictured during his playing days at Liverpool. (Image: PA)
Former Spurs and Brentford boss Thomas Frank was linked to the Fulham job, while ex-Ipswich boss Kieran McKenna was mentioned before taking a break from the game.
The West London club are now entering their fifth consecutive season in the top-flight, having finished 11th in the table last season.
"It is a real honour for me to be embarking on this new stage at Fulham FC, the oldest club in London," Arebloa said.
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"I feel a great sense of responsibility and I'm deeply grateful to Mr. Khan and Tony Khan for the trust they have placed in me with Fulham in the Premier League.
“I am really looking forward to experiencing the atmosphere at Craven Cottage with Fulham fans and beginning pre-season with the players next week. I am sure we are going to enjoy an incredible journey together."
Fulham become the eighth Premier League club to appoint a new boss this summer.
The others are...
Bournemouth - Marco Rose
Chelsea - Xabi Alonso
Crystal Palace - Pierre Sage
Ipswich Town - Gary O'Neil
Liverpool - Andoni Iraola
Manchester City - Enzo Maresca
Nottingham Forest - Oliver Glasner