The 37-year-old former New Zealand forward will continue to be part of the playing staff next term.
He succeeds Alasdair Dickinson, who is returning to his native Scotland for personal reasons in the summer.
Dickinson moved to the Ashton Gate club last summer on a three-year deal having been Scotland's scrum coach since 2018 after retiring from playing.
"Jonny has been planning and preparing for a few years to transition into coaching so I'm very pleased to add Jonny to our coaching team from next season," director of rugby Pat lam told the club website.
