Jones opted not to return to Christchurch for a second season with the Crusaders and Canterbury this year.
Ellison's responsibilities will involve assisting with team defence and position-specific player development.
Ellison, 37, made his Super Rugby debut for the Blues in 2005. He finished with 113 games during stints with the Hurricanes from 2006-10 (53 games), the Highlanders in 2012-13 (23) and his last 36 Super Rugby games with Melbourne's Rebels across 2014-16.
He had two stints with Ricoh Black Rams in Japanese rugby making 57 appearances.
A Commonwealth Games gold medalist for Sevens, a New Zealand Under-21 representative and several times a member of Māori All Blacks sides between 2005-09, he made his All Blacks debut against Italy in 2009.
He was a player-coach for Kurita Water Gush before being part of the Wellington Mitre 10 Cup coaching group last year.
Ellison said: "This is a really exciting opportunity for me to coach at Super Rugby level, as part of a world-renowned team that is full of talented players and coaches.
"I look forward to meeting everyone, and sharing some of my experiences as a player, both here in New Zealand and overseas. I have no doubt I'll learn a lot in this Crusaders' environment and I can't wait for the challenge ahead," he said.
Crusaders head coach Scott Robertson said: "Tamati is well-respected on and off the field, and we're excited to have him add his experience to our coaching group this season.
"He's a man with a lot of mana, and I know he'll make a significant contribution, sharing the experiences he had throughout a long playing career as he makes the transition to coaching."
Tamati Ellison arrived in Christchurch over the weekend and begins pre-season training with the side today (Monday NZT).