The 24-year-old right-back has admitted his disappointment at the way Rangers’ 2015-16 campaign finished.
Mark Warburton’s side lost 3-2 to Hibernian in the final of the Scottish Cup at Hampden Park in Glasgow this month.
The Gers, though, did win the Scottish Championship title with ease this past season and will feature in the Scottish Premiership during the 2016-17 campaign.
Rangers also clinched the Scottish Challenge Cup this past season to complete a domestic double.
Tavernier, who joined Rangers in the summer of 2015, has thanked the Ibrox faithful for their support throughout the season.
The former Newcastle United and Wigan Athletic man has also shared his hopes of a successful 2016-17 campaign in the Scottish Premiership.
So disappointed how the season finished! A bad end to what has been a great season for the club.. We'll come back even stronger!! 1/3— James Tavernier (@James_Tavernier) May 26, 2016
I really want to thank you for your outstanding support this season. It has been a pleasure to play in front of such special fans! 2/3— James Tavernier (@James_Tavernier) May 26, 2016
Rangers have a strong squad, and the addition of former Newcastle United and Manchester City midfielder Joey Barton is certainly going to help them in their quest to have a successful 2016-17 Scottish Premiership campaign.