The 25-year-old, who can play at right-back and in midfield, has agreed a two-and-a-half year deal.

Polster, who has trained with Rangers this month, won his only international cap to date in a friendly against Bosnia last year.

Meanwhile Jordan Rossiter is in talks about a loan move away from Ibrox.

Manager Steven Gerrard believes the midfielder, 21, will be the only departure this month, saying he does not "expect anyone else to go anywhere".

Gerrard, who has recruited Steven Davis and Jermain Defoe this month, does not anticipate pre-contract signings Glen Kamara and Jordan Jones will become Rangers players this month.

Dundee are keen to hasten Kamara's departure for a fee, but Kilmarnock have no intention of selling winger Jones

"Where we sit right here, we assume that Glen and Jordan will join us next season," Gerrard said.

'Couple of different clubs' talking to Rossiter

Jordan Rossiter (right) has made 11 Rangers appearances in two years

Rossiter, who has been plagued by injury, has only made 11 appearances in two-and-a-half seasons since arriving from Liverpool and is poised to leave Ibrox for the rest of the season.

"There is a good, strong possibility he could go out on loan," Gerrard added.

"He is speaking to a couple of different clubs and hopefully we can get him out, for the boy's sake, to go and play and get regular games.

"He has missed a lot of football, so I'm hoping to find the right solution for Jordan to get more game time."