The Scotland international has agreed a three-year contract and arrives from Besiktas for an undisclosed fee ahead of City's Premier League return.
The transfer - still subject to international clearance - ends McGregor's 12-month spell in Turkey, where he started 27 games for Besiktas following a move from Rangers.
He told the Hull website: "I'm really excited to be here and I'm happy that everything is done now.
"I can't wait to get started here. This is a great chance for me to play in the Premier League and I'm looking forward to the season ahead."
McGregor's arrival at Hull follows last week's permanent deal for Egypt winger Ahmed Elmohamady and the signings of defenders Curtis Davies and Maynor Figueroa.
The move also ends Steve Bruce's search for a new keeper after David Stockdale returned to parent club Fulham at the end of last season.
Forward Sone Aluko was quick to welcome his former Gers team-mate to East Yorkshire, writing on Twitter: "Buzzing McGregor has signed for us! Top class keeper and what a guy! Welcome to Hull Greegsy!!"