The 19-year-old did not make any appearance for Wolfsburg's first team in the Bundesliga this season but had been impressive with the youth outfit in the Regionalliga, making twelve appearances and scoring one goal.
He was initially linked with a move to Championship side Aston Villa but opted to join Everton.
Donkor admitted his excitement following the opportunity to experience English football with Everton and says he will develop into a better player as a result.
"I'm very happy and grateful to be here. I know this is a great club and I like the way they play," Donkor told the club's website.
"I'm looking forward to challenging myself in English football. Finch Farm is an impressive place. The facilities are great and I'm looking forward to getting started here.
He added: "I think I can learn from the good young players that are already here and hopefully we can be successful together."
Although, Donkor has represented Germany at youth level in the past, he is still eligible to represent Ghana at the senior level like Kevin-Prince Boateng, since his parents are from the West African country.