Rosser, 21, has put pen to paper on a contract extension to stay until at least 2022 and becomes the sixth player to sign new terms at the region. Knoyle, 28, has signed a new deal that will see him remain at Rodney Parade until at least 2020.
He has previously played for Gloucester Rugby as well as Ospreys, Scarlets and Cardiff Blues – becoming only the third player to play for all four professional Welsh regions when he joined the Men of Gwent.
“It’s great to see Tavis back from a frustrating injury period and returning to his high standards,” said interim Dragons head coach Ceri Jones.
“We know that, at his best, he can compete with any nine in Wales. Tavis is massively passionate about this region and one of our leaders going forward.
“His enthusiasm for the game and determination to improve is as strong as ever. He has relished the competition for the jersey this season and is very good at working with the young scrum halves in our set-up, passing on his knowledge and experience.
“It’s fantastic that he remains with us.”
A Dragons Academy product, who came through the Under-18s and Under-16s age grade sides, Rosser made his senior debut against Leinster in 2017.
Rosser underlined his attacking treat when he scored a hat-trick in the Guinness PRO14 against Zebre in April 2018 – becoming only the fifth player to score a hat-trick in a senior game for Dragons. The former Abersychan School student also showcased his talents in the Celtic Cup earlier this season when he scored five tries against Connacht Eagles at Ystrad Mynach.
A potent attacking force, Rosser has now scored 13 tries in 39 appearances for Dragons.
“Jared has had a really positive season and shown the rich promise that we all know he has,” said Jones.
“He has had some real standout games, such as the Ospreys derby match at Rodney Parade, and is definitely one for the future who can really kick on. Jared is a Gwent boy, proud to be part of this region, he has come through our Academy system and continues to improve year on year.
“We’re all excited to see how he develops over the next three years and thrilled that Jared will be a key figure as we look to push our region forward.”
