Bristolian Tavare, 26, has signed until the end of the 2019 season, whilst van Buuren has signed until the end of the 2018 season.
Head coach Richard Dawson said: “It’s great to see both players committed to the club for the long term.
“Will and Graeme are two players who are still developing their skills and both will add strength and depth to the squad in all competitions.”
Tavare said: “I’m obviously delighted to sign a two year extension with my boyhood club.
“After a tough summer with injury and not performing as I would back myself, the constant kind words from the supporters throughout the summer make you realise how much of a family this club is.
“The coaches and players are all pushing in the right direction and I am so excited to start the next season with a seriously talented bunch of lads.”
Graeme, who hit a magnificent 172 not out in the County Championship win against Worcestershire, added: “I have had an awesome time at the club this year and loved every minute of it on and off the field.
“I am over the moon and very grateful to be spending the next couple of years in Bristol and can’t wait for the 2017 season to start.”