The 37-year-old Scot will replace ex-club captain Alex Rae, who leaves the role at the end of the season.
Tunnah played as a hooker in Scotland before retiring in 2010, after serving a five-month suspension for failing a drugs test.
"It will be great to be working at a fully professional club where there's a real aspiration to succeed," he said.
Tunnah has coached in Australia since he stopped playing, spending some time working with ex-Australia flanker Jim Williams at National Rugby Championship side Greater Sydney Rams.
Reds head coach Harvey Biljon added: "He has a big task ahead given our reputation for having a strong pack in recent seasons, but that's a challenge he's excited about and I see him rising to.
"With a number of departures in May he has the opportunity to mould a new pack."
Rae, meanwhile, has agreed a playing contract with Bedford Blues for next season.
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Jersey Reds have appointed Australia-based Neil Tunnah as their new assistant coach for next season.