Rangers are making further bids, with reports claiming Brighton have rejected an initial offer for centre-back Connor Goldson.
The veteran goalkeeper was offered a new deal by Hull City upon expiry of his contract at the KCOM Stadium and had other options on the table, but he insists that the chance he thought would never come to return to the club he left in 2012 is a dream come true.
The 36-year old played a key role in the The Tigers squad in the 2017/18 season, featured in all 46 league games for Nigel Adkin's side.
McGregor is now Steven Gerrard's second signing since taking over as Rangers boss, following the capture of midfielder Scott Arfield from Burnley earlier this week. It's obvious that he is below the required level in the Premier League and it was hard to judge how he would have done in the club's promotion winning campaign past year as he underwent heart surgery and missed a lot of action.
"I have played against Allan a number of times in my own career and I know just how fierce a competitor he can be".
"I'm buzzing and can not keep the smile off my face", he told Rangers TV.
"I started training here when I was 12 years old".
He has a spell on loan at Cardiff City a year ago and has 35 caps at worldwide level with Scotland to his name.
"We need to make this place a fortress where nobody wants to come", he said.
"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".
He joined Hull when they were in the Premier League and helped them qualify for the Europa League for the first time.