Financial details were not disclosed but British media reported the Saudi Pro League champions paid 40 million pounds ($51.33 million) for the player.
Al-Ittihad posted a video on messaging platform X, formerly known as Twitter, with the title "Tigers are permitted to pass" in reference to media reports suggesting the deal might be delayed due to the breed of Fabinho's dogs which are prohibited from entering Saudi Arabia.
The video featured the Brazilian midfielder holding a tiger and saying: "I'm Tiger."
"Today I leave my home. It's been five years wearing this jersey and always with the greatest honour and happiness possible. I love this club. Thank you, Reds, for everything we've experienced together. You will never walk alone," Fabinho wrote on X.
Fabinho will join Ballon d'Or winner Karim Benzema and former Chelsea midfielder N'Golo Kante at the Jeddah-based club.
The Brazil international made 219 appearances for Liverpool since his arrival in 2018, and helped the team to the Premier League, Champions League, FA Cup, League Cup and UEFA Super Cup titles.
Jordan Henderson also left Liverpool last week to join Steven Gerrard's Al-Ettifaq in Saudi Arabia.
The Saudi Pro League has become an attractive destination for high-profile players since Cristiano Ronaldo moved to Al-Nassr last January in a deal reported to be worth around $220 million per year.
