Strachan junior had been Darren Ferguson assistant director of Peterborough and Celtic compensation to secure his release.
He will now work under Neil Lennon and assistant to boss John Kennedy.
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“It is a great honor to be appointed to this position with Celtic, like a giant of a club and a real emblematic of football institution – it is truly an opportunity that I simply could not refuse”, said Strachan.
“I am very excited about starting out with Neil, John and the players that we are ready for the challenges ahead.
“Neil and John have been massive on numbers in the nine-in-a-row travel club and it will be fantastic to be part of a management and team coaching team.
“The club has had a series of successes over the past few years and I know everyone at Celtic and our supporters are doing everything we can, together, to keep this race going.
“I know we are facing a really exciting season and for me personally it is a great time to join this brilliant club. I will work my best every day to bring success to the club. ”
Lennon, who played under the father’s Strachan for Celtic, added: “We are delighted to bring Gavin to Celtic music, he’s great for us and someone I know works really well with myself, John Kennedy, the players and the rest of our backstage team.
“We have had a number of options for the role, but He has the outstanding candidate.
“He is really talented, experienced, hard working and respected coach and I know he has the qualities to make a great contribution to the club. We are all very happy to welcome Gavin from our team. “
Aberdeen-born Strachan began his career in Coventry when his father was in charge, and made 23 appearances for the club, scoring a goal.
He had ready spells with Dundee and Motherwell before playing for likes of Hartlepool and Notts County.
After hanging up on his crampons, he had a period as non-League manager Ilkeston, before coaching roles under Ferguson at Peterborough and Doncaster Rovers.