Adey, a Canadian, had been working in Italy before signing with the Northern Ireland side.
The 49-year-old is no stranger to the British league, having played with the Nottingham Panthers and Sheffield Steelers.
On leaving the Panthers, the side retired his jersey and Adey made it into the British Ice Hockey Hall of Fame.
It’s great to be in a rink where there’s passion and a great atmosphere for the players, and your home fans are buzzing every night, and that’s a positive for us.
Giants boss Todd Kelman described him as his "first choice" for the role and Adey said it was an opportunity "to work with a very professional organisation and a great rink, a great city".
The new coach added: "My job is to get the team to win and try to win trophies. That's expected.
"Not everyone can win a trophy, every year but our goal will be to at least try to win one trophy every season."
Adey said that his coaching style will be proactive, describing himself as an "offensive-minded coach" who is "not afraid to go for it".
Recruitment has been well underway for the Belfast side in recent weeks, re-signing captain Adam Keefe, forward Mark Garside and defenceman Davey Phillips.
On Thursday, the Giants revealed they also re-signed goaltender Stephen Murphy, forward Colin Shields, and defenceman Robby Sandrock for a further season.
We have the nucleus of our team back next season.
Kevin Phillips, brother of Davey, has also been snapped up again - having previously been a Giant before spending three seasons with the Braehead Clan.
"I have kept my eye on him over the last few seasons and we need to add another non-import defenceman and, to me, Kevin is a perfect fit for us," Todd Kelman said.
"I know what he can do and what he has done in this league. He is very reliable and he has matured into a great player.
"We are lucky to have him and I have to admit that having the opportunity to play on a team again with his brother was a key factor in his decision to return to Belfast."
But while Adey hinted at more signings in the future, he said they will be carefully thought out.
"It takes time. We want to make sure we get the right people, so I don't think we need to rush ... It's still early," he explained.