The 32-year-old arrived at Sandy Park in 2015 after spells at both Bath and Leicester, as well as in Super Rugby with the Brumbies.
Having won the Premiership title in 2013 while at the Tigers, Salvi was part of the Exeter squad who helped the club win their first ever domestic title in 2017.
After seeing his playing chances diminish in recent months, Salvi has now called time on his career after 53 appearances for the Devon outfit, admitting he could not ignore the opportunity to join the coaching staff.
"As a player you never want to have that day come where you have to hang your boots up," he told the club's official website. "However, this opportunity that Rob and the club have offered me was one I simply couldn't turn down.
"To be involved with the Chiefs moving forward, it's a great privilege for me and one that I am very excited about. To be part of what the Chiefs have achieved in the past few years has been outstanding, but I do feel there is still a great more to come from the team moving forward.
"What we have here, however, is a very special group, some may call it a bit odd, but every one of the guys is fiercely determined to do well and achieve things as a collective unit."