Stewart has been constantly linked with a move to Ibrox and now the deal has finally seen the light.
The 29-year-old, who recently ended his loan spell with Aberdeen, has agreed on personal terms with the Light Blues for the next two years.
The Scottish forward signed for Blues in 2016 and has had his loan spells with Kilmarnock and Dons, bagging eight goals in 16 appearances with the former club.
A youth product of the Light Blues, Stewart rose to prominence during his four-year spell with Cowdenbeath, where he garnered 40 goals in 141 appearances.
Future plans at Ibrox
Stewart will never be a guaranteed starter as he is cited as the second choice.
However, the Scotsman will battle for his place with Defoe, who is currently on loan from Bournemouth. The ex-English international turned out to be a perfect back up for Morelos in his absence.
With the acquisition of Stewart, Steven Gerrard has completed a handful of signings over a short time. Jake Hastie and Sheyi Ojo are also due to arrive this summer.
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The Ibrox gaffer is aiming to compete with their arch-rivals Celtic for title glory next season.