Toure has signed a one-year contract with the side that finished 11th on the table last season.
The 38-year-old recently left his role as assistant manager at Ukrainian side Olympik Donetsk.
A club statement from Grozny read: “Former footballer Yaya Toure has joined the coaching staff of the Thunderbirds. Head coach Andrey Talalaev will determine his duties as an assistant.”
“The contract with the specialist is calculated until the end of the 2021-22 season.
“Yaya has played for teams such as Beveren, Metalurh Donetsk, Monaco, Olympiacos, Barcelona and Manchester City.
“We welcome Yaya Toure and say to him: 'welcome to Ahmat.'”
Toure, who is a four-time African footballer of the year, spent eight seasons with Manchester City where he won three Premier League titles, one FA Cup and two League Cups.
Toure also played for AS Monaco and Barcelona, where he won the 2009 UEFA Champions League and two La Liga titles.
He was a member of the Ivory Coast national team that beat Ghana on penalties to win the 2015 African Cup of Nations.
