The 24-year-old, who scored 13 goals in 69 appearances for the Owls, has moved to the City Ground on a three-year deal.
Sky sources learned on Tuesday that the Reds were targeting Antonio to add pace to their promotion challenge.
And Forest chairman Fawaz Al Hasawi tweeted on Wednesday: "I am pleased to announce Michail Antonio as our latest signing. He has arrived from Sheffield Wednesday on a three-year deal."
Antonio helped Wednesday win promotion to the Championship in 2012 during a season-long loan spell from Reading, before the move became permanent that summer.
He became a key player for the South Yorkshire club and his performances alerted the interest of a number of other clubs, some of which were understood to be in the Premier League.
It will come as welcome news to Forest manager Stuart Pearce, who was involved in a dispute with chairman Al Hasawi earlier this week after key players Karl Darlow and Jamaal Lascelles were sold to Newcastle.
The duo have subsequently been loaned back to Forest for next season and Pearce will be further appeased by the arrival of one of his principle targets.