He also held talks with English Championship clubs Blackburn Rovers and Sheffield United but Rangers’ proposal swayed him towards staying in Scotland.
Souttar, 25, is out of contract at Hearts this summer and available to join another club for free. He verbally agreed terms on a long-term deal with Rangers after meeting manager Giovanni van Bronckhorst and director of football Ross Wilson.
It is understood the lure of Champions League football was a major factor in his decision in addition to challenging for the Scottish Premiership title.
Hearts offered the centre-back a new deal in an effort to keep him in Edinburgh but he decided to leave several weeks ago, alerting clubs on both sides of the Border.
A formal announcement on the move is expected in the next few days, which will then leave Hearts to decide whether to try and sell Souttar and recoup some cash before the January transfer window closes.
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.
Souttar suffered three ruptured Achilles during his time at Tynecastle but has stayed injury-free and played consistently since returning to action last April.