Stewart who plays on loan at Aberdeen has been persistently chased by the Gers for a while now.
The announcement is expected to happen at the end this season.
Stewart, 27, progressed through the youth ranks of the Light Blues and Hearts.
However, he came into prominence during his four-year spell with Cowdenbeath, where he played more than 100 matches and scored 30 plus goals.
The Scottish forward also had a decent spell at his country club Dundee with 71 appearances and 22 goals before joining Birmingham.
He was then loaned to Aberdeen and Kilmarnock the subsequent seasons and fared well with the latter club, scoring 8 goals in 16 appearances.
How will Stewart fit in Gerrard’s playing 11?
Stewart, as of now, is having an underwhelming spell with the Dons, scoring only one goal in 13 appearances.
The striker has struggled to become a starter in Deren McInnes’ playing 11.
And now the Gers can benefit well from the Scottish forward, with his abundance of experience.
Though it is difficult to beat the likes of Alfredo Morelos for a starting place, Jermain Defoe and Stewart can provide cover for the Colombian striker.
With Defoe being bound to his parent club Bournemouth, Stewart can soon become Steven Gerrard’s second choice striker.
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The Light Blues picked up another comprehensive win against the Dons on Sunday and Stewart appeared as the substitute for the game.
James Tavernier scored two penalties, as the Gers wrapped up the game 2-0. And the victory marked their third in a row and they are second in the Premiership table.