The 111-cap flanker, who turns 36 next month, will join the Brisbane-based side for the 2017 and 2018 seasons while also playing for Suntory Sungoliath in Japan's Top League.
Smith's capture will fill the hole left by openside Liam Gill, who has decided to leave Australia for French club Toulon at the end of the season.
It is a major coup for the Reds, who have endured a miserable few seasons since they won the Super Rugby title for the first time in 2011.
Australia captain Stephen Moore has also signed up to move to Brisbane from the ACT Brumbies next season and was delighted to hear the news.
"Well at least I won't be the oldest bloke in the squad next year," the 33-year-old joked a news conference on the eve of Saturday's test against England.
"It's great, he's a legend of Australian rugby and you've seen even this year how well he's played for Wasps in England.
"He continues to amaze with how well how he can play year after year. He's a great addition not only for what he can do on the field but off the field with the young players."
Evergreen Smith enjoyed a stellar 2015-16 season with English Premiership side Wasps and was named the Players' Player of the Year in England last month.
"The body feels great and the experience in England has been outstanding," Smith said.
"I'm really looking forward to playing Super Rugby again."
Reds executive Daniel Herbert later suggested that former Wallabies flyhalf Quade Cooper would be welcomed back with open arms if he decided to leave Toulon and return to Australia.
"There's room if the desire's there," he said. "We don't like to comment until things have been solidifying but there's room.
"I'm an unashamed fan of Quade, have been for a long time..."
Cooper is a cult hero in Queensland because of the role he played in that 2011 triumph but he clearly has one significant fan in New South Wales as well.
Wallabies coach Michael Cheika said Cooper was one of a string of players he had been working to try and persuade to return from Europe.
"I've been doing more than endorsing it, I've been out there trying to get him back," he said in a crowd-pleasing comment at a Reds function in Brisbane on Friday.
(Editing by John O'Brien)
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