According to the BBC website, McGregor had a fresh offer from Hull City on the table but instead of signing a deal with the Championship side, he decided instead to make the move to Scotland.
The keeper was out of contract at Hull and turned down the offer of a new deal from the club.
McGregor's return places doubt over current No 1 Wes Foderingham's future.More news: Preakness 2018 Draw and Odds: Justify Is Overwhelming Favorite
He described the lure of returning to Rangers, where he believes he has unfinished business, as too strong to resist.
The 38-cap Scotland global won three league titles, a hat-trick of Scottish Cups and five League Cup titles during his first Rangers stint. He lifted 11 trophies in total for the Ibrox club. It does. I started training here when I was probably 12. "To be back is incredible".
"I can't keep the smile off my face", McGregor added.More news: IPL 2018: RCB Vs SRH - Five players to watch out for
The Argus reports that Rangers have identified the 25-year-old as a key target as Steven Gerrard continues to conduct an overhaul of his squad after the Gers finished third in the Scottish Premiership this season. But once there is a wee sniff it could happen, then obviously it's exciting.
"Every game is an opportunity for three points and if you keep doing and doing that and doing that, as we've seen before that's what wins titles". It came as a surprise.
"You need to win games and it doesn't matter who you are playing". Someone gave me a shout two or three weeks ago to say Bomber (John Brown) wanted my number.More news: Microsoft formally announce the Xbox Adaptive Controller
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