The 27-year-old goalkeeper is a free agent at the moment, with his contract with Lech Poznan having run out at the end of last month.
According to The Daily Record, Gostomski will sign a six-month deal with Rangers later today.
The Polish goalkeeper has expressed his delight at the chance to play for the Gers, and has said that he wants to make himself a first-team regular for the Scottish giants.
“I’m delighted to be here,” Gostomski told The Daily Record. “I had options but this is a great opportunity and with my experience I think I can bring something to Rangers.
“They are a huge club with a great history and I want to be part of that. I know there are good goalkeepers here already but I want to play and fight for a place in the team.”
Rangers are at the top of the Scottish Championship table at the moment with 47 points from 19 matches.
Mark Warburton’s side are three points clear of second-placed Falkirk and also have a game in hand.
The Gers have the best squad in the Scottish Championship and are favourites to get automatic promotion to the Scottish Premiership at the end of the season.
Rangers will take on Cowdenbeath at Ibrox in Glasgow in the fourth round of the Scottish Cup next weekend.