The Scotland international has signed a pre-contract agreement with the Ibrox club who beat off interest from several English Championship sides including Blackburn Rovers and Sheffield United to land the 25-year-old.
Souttar is out of contract at Hearts this summer and was available to join another club for free. He agreed terms on a long-term deal with the Scottish champions after meeting manager Giovanni van Bronckhorst and director of football Ross Wilson.
Confirming the move, Wilson said: “We are really looking forward to John joining Rangers and continuing his development under Gio, our coaching and support staff.
“John is a full Scotland international and has so much potential ahead for the coming years. I have really enjoyed getting to know John across all of our conversations so far and I can see how excited he and his family are to be joining Rangers. We are equally excited to welcome John to Ibrox.”
Hearts offered the centre-back a new deal in an effort to keep him in Edinburgh but he decided to leave several weeks ago.
The lure of Champions League football is believed to have been a major factor in Souttar’s decision in addition to challenging for the Scottish Premiership title.
Rangers may be willing to do a deal this month but Tynecastle officials are adamant they will not sell one of their most influential players on the cheap.
They paid £120,000 to sign Souttar from Dundee United back in 2016 and will want a substantial transfer fee to do any quick deal with counterparts at Ibrox.
A club statement read: "Heart of Midlothian Football Club notes Rangers Football Club’s announcement of John Souttar’s pre-contract signing.
"The club reiterates that John is an important member of the first-team squad and will remain so until the end of the season unless a significant and satisfactory offer is made during the January transfer window.
"No further comment will be made at this time."
Souttar suffered three ruptured Achilles during his time at Tynecastle but has stayed injury-free and played consistently since returning to action last April.