The 21-year-old spent the second half of the 2020/2021 season on loan at Liverpool after they lost the likes of Virgil Van Dijk, Joel Matip and Joe Gomez to injury.
Kabak made 13 appearances for the Reds in his short stay at Anfield, helping Jurgen Klopp’s side secure a top four finish following a difficult start to the season.
Norwich City have the option to make Kabak’s move permanent for €13m at the end of the season.
"I'm very happy to be a part of this family," Kabak told the club's website. "I'm looking forward to playing in front of the fans and getting some points.
"I spoke with the head coach and I'm really impressed by his project and what he said to me. I believe in him and his project.
"I played in the Premier League last year and I really enjoyed it. So, I want to play again and that's why I'm here. I want to play in the Premier League and to give something to the team.
"I'm looking forward to playing in front of the fans with this jersey. We will work hard to get some wins and take some points to make our fans happy."
Kabak was part of the Turkey squad at EURO 2020 but did not play in any of their group stage games.
Norwich City have started their Premier League campaign with three straight losses to Liverpool, Manchester City and Leicester City.