The midfielder's contract is expiring at the end of the season, meaning he will make the switch to the Volkswagen Arena on a free transfer.
It was suggested last week by kicker that the deal was done, and Wolfsburg announced that they had tied Didavi done to a four-year deal.
Crucial to Stuttgart
Didavi had made 164 appearances for the Swabian side to date, scoring 47 goals across the under-19s, reserves and first-team.
His breakthrough came when loaned out to 1. FC Nürnberg during the 2011/12 campaign, where he found the net nine times in 23 Bundesliga games.
The two seasons that followed failed to get anywhere near those heights, with game time limited due to a fractured ankle and other niggling problems.
However, he came up trumps at the end of last term. Seemingly destined for the drop, Stuttgart won their final three games to stay up; Didavi scored twice in that time.
Now with some match practice and a pre-season behind him, Didavi has netted 10 goals and added five assists to become Stuttgart's creative spark this year.
Didavi and Dutt give their thoughts
Understandably Thomas Dutt, Stuttgart's sporting director, was devastated to lose their main man, admitting it was "no secret" they want him to stay.
Dutt said the club have "intensively attempted to convince him to stay" through the season, though wished him well "with a heavy heart".
"I have a lot to be grateful to VfB for. The club has become a part of my life, which you don’t just easily let go of," commented the departing Didavi.
He added, "I am convinced that the move to VfL is exactly the right step for me, because Wolfsburg are chasing the very highest sporting ambitions."
Quotes via VfB Stuttgart and VfL Wolfsburg