A former Royal Grammar School student, Arr impressed throughout last season in the Warriors Academy and A League and was called up by England Under-19s.
This season the 19-year-old has been in action for England at Under 20s level, successful achieving the Grand Slam in the Six Nations, and has made six appearances from the bench for the first team at Warriors.
Director of Rugby, Mike Ruddock, said: "We are delighted to announce that Jonny Arr has signed for one year.
"Jonny has had a good season playing regularly for the A team, playing for England Under 20s and also coming off the bench on several occasions for the first team, including last Saturday in our victory over Gloucester.
"He is held in very high regard at the club and in many ways reminds me of a young Robert Jones in terms of his speed of pass and thought.
"I predict a big future for Jonny Arr and hopefully next season he continues to make even more progress."
Arr said: "I'm pleased to have committed my future to Warriors for another season and look forward to continuing my development under the guidance of the coaching team here.
"I have been connected to the club for over a decade, since my involvement with the mini/juniors. It has always been my dream to play for the first team and this year that has become a reality, I have enjoyed every second of action playing for Warriors.
"My game has developed with the support of the coaching team and also the new style the club is looking to play. I hope I can now be a big part of a successful future here at Sixways Stadium."