The German has signed a four-year contract believed to be worth £85,000 a week and his departure comes as Chelsea signed Juan Cuadrado from Fiorentina for £27m.
There were fears that Schurrle’s move would not go through before the German transfer window shut at 5pm UK time.
A tweet from the Bundesliga club confirmed the move, saying: ‘Finally – pen has been put to paper! @Andre-Schuerrle makes the move from Chelsea to the Wolves. Contract until 2019.’
Schurrle has changed his Twitter biography to ‘VFL Wolfsburg’.
The 26-year-old was one of the players of last year’s World Cup and looks set to join from Fiorentina for a fee which will reportedly rise to his £26.8million release clause.
Cuadrado was at Stamford Bridge on Saturday for the 1-1 draw with Manchester City, while the move saw Mohamed Salah move the other way on loan.
The two clubs had been stuck in talks over a solidarity payment owed to club’s in Schurrle’s development, with neither wanting to pay five per cent of the transfer fee.
It is still unclear how the disagreement has been resolved.
Schurrle needed to beat a noon deadline to be registered on the German FA’s transfer list before potentially completing a switch. That was done under an hour beforehand as the move went down to the wire.