The duo's present contracts expired at the end of the current campaign and they have been told they can leave on free transfers.
Russian winger Kanchelskis and Australian international Vidmar have failed to hold down regular places in the Gers starting line-up and Alex McLeish has allowed them to leave Ibrox.
McLeish paid tribute to their efforts this season and suggested that the search for first-team football was the main reason for their departures.
"Andrei and Tony are leaving. They're free to go under Bosman as they won't be offered new contracts," McLeish told Rangers News.
"Both have done a great job for me this season. Tony can play anywhere in defence and we have also put him in midfield.
"When Andrei came into the side, his attitude was fantastic. I saw him in the Under-21s and he looked like he had given up on football.
"But a lot of foreign guys only come alive when they are involved in first-team football.
"Theirs is a mentality we perhaps don't understand in Scotland. We sometimes have to adapt to them as much as they have to us."
Vidmar has previously expressed a desire to play in England and he could be set for a move down south while there is expected to be no shortage of offers for former Manchester United and Everton ace Kanchelskis.
