The American has put pen to paper on a two-and-a-half year deal and becomes the club’s fourth permanent signing of the January window and the sixth in total.
Polster had been on trial with the club and clearly impressed Steven Gerrard enough to warrant an offer of a contract.
Polster will now come in to provide competition in midfield and also cover at right-back with that being a secondary position.
With Gerrard having now signed two new midfield players in Polster and Steven Davis, one Ger may well be worrying about his potential playing opportunities.
The beginning of the end for Coulibaly?
Lassana Coulibaly started off the season brilliantly from Rangers following his loan move from French side Angers.
His dynamic start was interrupted by injury around a month into his Ibrox stint, and he simply hasn’t been the same player since returning in September.
He’s had plenty of time and opportunites to rediscover his form but it hasn’t happened for the Mali international.
Gerrard going out and signing two new midfield players makes for bad news for Coulibaly, who will surely now struggle to get regular game time.
Ovie Ejaria’s stint was cut short, but there is still strong competition in the form of Ryan Jack, Scott Arfield, Ryan Kent, Ross McCrorie and Andy Halliday.
Gerrard could yet add another midfielder in the form of Glen Kamara before Thursday’s deadline, the Dundee star has been strongly linked with a mid-season move by the Evening Telegraph.