As yet, the 41-year-old defender has refused to reveal the identity of his new club, although his next employers are believed to be based in England.
"It will be an emotional week because it's the end of five years for me at Rangers, five years I have loved," Weir told the club's official website. "I'm not sad about it, I'm happy that I got the opportunity to play for such a great club.
"I have so many memories to look back on and I am very proud of that, I wouldn't change it for the world.
"But it's not been a difficult decision, if anything I probably prolonged it."
Weir joined the Gers in 2007 from Everton.