The promising winger was today short-listed for the PFA Scotland Young Player of the Year award after an impressive breakthrough season with the Fir Park club.
Hastie, 20, is out of contract in the summer but Rangers will be required to pay compensation to Motherwell.
He was part of the Motherwell side which won the Scottish Youth Cup in 2016 and is now a Scotland Under-21 international.
After loan spells at Airdrieonians last season and Alloa in the first half of this campaign, Hastie has flourished under Stephen Robinson at Motherwell, scoring seven goals in 14 appearances since January.
He won Premiership Player of the Month for March.
Rangers manager Steven Gerrard told the club’s website: “We’re delighted to be able to add Jake to the squad next season. We are always looking to add individuals to our group of players who will improve us and Jake will undoubtedly do that.”