The American international impressed Steven Gerrard on trial and has done enough to earn a permanent move from Chicago Fire to join Rangers subject to international clearance.
Gerrard had revealed on Tuesday that a deal to bring the 25-year-old defender to Glasgow was imminent, after securing a work permit, and the move was confirmed after a four-year stint with Chicago in MLS.
Polster has one cap for the US national team, coming in a friendly against Bosnia in January 2018 and is the latest American to sign for Rangers, following in the footsteps of players such as Claudio Reyna, DaMarcus Beasley and Carlos Bocanegra. He will provide cover with the likes of Connor Goldson injured.
A statement on the club website said: “Rangers are today delighted to confirm the signing of Matt Polster subject to international clearance.
“Polster joins the club from MLS club Chicago Fire on a two-and-a-half-year deal.
“The 25-year-old can play both at right-back and in midfield, and has been capped once for the United States national team.”
Polster told Rangers TV: “It’s something I have always dreamed about doing.
“As a little boy a lot of people will know that I always wanted to play in Europe, even before going to MLS. To finally do it for this type of club, I’m speechless.
“Now it’s all signed and sealed, I’m ready to play.”