The 33-year-old also has worldwide experience, having racked up 97 caps for Slovakia.
McGregor, who has 38 worldwide caps, moved to Hull after a year in the Turkish top flight.
Rangers have already seen David Bates agree to join Hamburg on a free transfer this summer and with periodical doubts over Bruno Alves' future, Gerrard may need to bring in a central defender.
He played all 46 league games as the Tigers finished 18th.
The veteran goalkeeper has signed a two-year contract at Ibrox Stadium to become manager Steven Gerrard's second signing.
Ebola spreads to urban areas in Congo, 23 dead so far
The vaccine, from US -based pharmaceutical firm Merck, is unlicensed but has been shown to be highly effective against Ebola. It involves vaccinating voluntary contacts, contacts of those contacts and health care and other front-line workers.
McGregor started his career at Ibrox and had loan spells with St Johnstone and Dunfermline Athletic before becoming a first-team regular.
Rangers are expected to make a number of additions this summer as they look to try and compete with Old Firm rivals Glasgow Celtic and could also be expected to sell a number of key stars to fund those deals.
McGregor said: "I can't keep the smile off my face".
"I started training here when I was 12 years old and used to come through the main stand maybe twice a week". "We need to win games, it doesn't matter who you're playing, every game is an opportunity for three points".
The Premier League side turned down a £600,000 bid for the centre-back yesterday and are likely to want more than £1m. Let us know what you think.
Manhattan Ends Prosecutions for Marijuana Possession
Hizzoner and the NYPD have taken a torrent of criticism over pot arrests targeting blacks and Latinos - most recently from Rev. De Blasio announced that over the next several months, the NYPD will be working to reform its cannabis enforcement policies.
Cyclists ride in silence to remember
Despite the rain, 200-300 bicyclists showed up for this year's Ride of Silence through the streets of Center City. Ride of Silence is a national event and bike shops across the USA conduct rides at the same time.
Collegium defers its decision on Justice Joseph
Lokur and Kurian Joseph - had unanimously recommended Justice Joseph as apex court judge in a resolution on January 10. Four other additional judges were also recommended by the Rajasthan High Court Collegium to be made permanent.
Eli Manning's Memorabilia Fraud Lawsuit Reaches Settlement
The email does not refer to the two helmets at issue in the lawsuit, but Inselberg alleged it indicated a pattern of fraud. Powers Jr. said attorneys instead will only begin picking the jury next Monday, in a process that may take several days.