Lawrence is out of contract having left Derby and has been looking for a new club in the ongoing transfer window.
The Welshman was expected to stay in England and Sheffield United were confident of adding him to their squad this week.
But the Blades are set to miss out on his signature as Lawrence is set to go north of the border to Scotland.
Rangers have managed to convince the player to make a move to Ibrox over Bramall Lane this summer.
Lawrence has given his nod to the move and Rangers are now finalising the deal to sign him on a free transfer.
Giovanni van Bronckhorst has been intent on adding more goals to his Rangers squad that finished second in the league last season.
The Welshman is a versatile attacker and has the ability to play in a variety of roles including up front, attacking midfield and left-wing.
He scored nine goals in 30 appearances for Derby last season and was one of their bright sparks in a disappointing campaign.
