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The right-back has scored 63 goals in 284 appearances since joining the Glasgow giants in 2015, including 17 this season as Steven Gerrard's men claimed a first top-flight title in 10 years.
"I am delighted to extend my contract at this magnificent club. As soon as I arrived six years ago, I soon realised how massive this club is," Tavernier told the club's website.
"It isn't a club really - it's an institution. To captain Rangers to our historic 55th title is a memory I will hold forever. It is a privilege and an honour to pull on the famous royal blue, and adding the captain's armband makes it even more special.
"I will continue to strive to be better as a player, captain and make sure we continue to set the standard higher than before - 55 wasn't the end of the journey, it was only the beginning."
Gerrard said tying down Tavernier was a sign of Rangers' ambition to remain on top in Scotland and progress in Europe.
"I am delighted to secure the services of our captain on a new long-term deal," the Rangers boss said.
"This shows the ambition of both James and the club as we continue to drive forward to fulfil our ambitions, both domestically and in Europe."
© Agence France-Presse