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.
"Jonny is a massive leader, mentor and player for the Bears, and he has played a big part in driving our culture and performance on and off the field.
"He has the utmost respect from the players and management alike and I believe he will be an excellent addition to the coaching team and he'll continue to add real value on and off the pitch."
Afoa, who signed a new one-year contract last month, added: "There's a significant responsibility and it's one that I'm relishing alongside representing the Bears on the field.
"We've developed a good reputation with our scrum so the impetus is on me to build on that and work with the guys to continue our growth in that area."
Lam praised the work that Dickinson has done in his short time at Ashton Gate, a period which has seen the Bears win their first European title when they beat Toulon in the Challenge Cup final last October, and sees them currently 12 points clear at the top of the Premiership.
"Dicko has added real value to our environment and to our game - the scrum has continued to improve and develop with his support and we have no doubt that he will continue to grow as a fine young coach," he said.
"We thank Dicko for the commitment he and his family have shown, particularly during these difficult and unprecedented circumstances in a pandemic.
"While we understand why he must return home to Scotland we are pleased he will be part of our big push to achieve our team goals for the rest of this season."