Former Arsenal and City defender Toure is now a fulltime member of manager Pep Guardiola's backroom team.
Viana told City's website: “We’re delighted to permanently add Kolo to our first team coaching staff.
“Not only does he bring his immensely precious experience at football’s elite level, but he also has a deep connection with Manchester City and a deep knowledge of the Club.
“We’ve also been hugely impressed with his work and success with our Under-18s, and by adding him into our senior staff permanently, this will only strengthen the transition for players in our Academy into the first team.
“As we already saw throughout his time with Pep Guardiola, Pep Lijnders and James French this summer, his massive personality of optimism and positivity is hugely infectious and we’re already looking forward to his work moving forward.”