The 26-year-old former Germany youth international had earlier in the day announced his decision to leave Stuttgart, the club he has played for since the late 1990s and joined as a young boy.
"The club (Stuttgart) has become part of my life and that is why this was a very difficult decision," said Didavi, who made his Bundesliga debut in 2010.
Didavi, who also had a loan spell at Nuremberg playing under current Wolfsburg coach Dieter Hecking, has played a key role in helping Stuttgart avoid relegation in the past two seasons.
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"We have to accept that with a heavy heart," Stuttgart sports director Robin Dutt told reporters. "Dida informed us of his decision during the winter break. It is no secret that we would have liked to tie him to us past this summer."
Didavi has scored 10 goals and set up another three to help Stuttgart to 12th spot, six points above the relegation zone with six matches left.
"Our goal now is to secure our spot in the division as quickly as possible," Didavi, a former Germany youth player, said. "I am convinced we can do that."
(Reporting by Karolos Grohmann; Editing by Toby Davis)
