The 23-year-old arrives from Croatian side NK Osijek who Rangers faced in Europa League qualifying and has signed a four-year deal, subject to receiving a visa and international clearance.
Grezda, an Albanian international with six caps, follows Joe Worrall in joining for the club on transfer deadline day and becomes the club’s 14th summer signing.
Rangers boss Steven Gerrard is keen to see the player light up Ibrox. Grezda missed both legs of the Europa League second qualifying tie against the Ibrox side.
“He is an excellent player and the fans will love him because he can contribute in the final third,” Gerrard told the Rangers official website. “He’s really quick, very direct and he comes in with international experience.
“According to Borna and Nikola Katic he was by a mile Osijek’s best player last season.
“He is a very dangerous player and while you never want to see anyone injured, we are thankful he wasn’t available to play against us. All going well, hopefully he’ll be a big player for us moving forward.”
Meanwhile, Gerrard hinted at further additions.
“I’m always looking,” he said. “It doesn’t shut till 12 so there is plenty of time.”