"The Bundesliga is the best league in the world and the best players also belong there," Boateng said.
"I'm delighted to be back home."
Born in Berlin, Boateng made his Bundesliga debut with
He returned to
He then joined Milan, for which he scored 17 goals in 100 games, including two against PSV Eindhoven in a UEFA Champions League play-off on Wednesday.
"We're really delighted to have been able to sign him because we've been working intensively on this for weeks," said Schalke's director of sport
"It was easy to convince Kevin to join us, but it was harder to convince Milan to sell.
"Kevin's done really well there and was a fans' favourite. He has great leadership qualities and we hope we will have a successful future with him."
Boateng will be ineligible for the Royal Blues in the UCL, having already appeared in the competition for Milan, but he is available to make his second Bundesliga debut against Bayer Leverkusen on Saturday.
A suspension which was hanging over him from his previous spell in the Bundesliga has been wiped out, meaning he is available for selection.
"I'm absolutely delighted that I can play for a top club like Schalke," Boateng said. "This is a new challenge for me."
Boateng's arrival does not mean
"I don't know why that should be more probable now," said Heldt in view of increased speculation the
"It would be schizophrenic to sign one quality player and then let another one go. That is not what we want."
Raja Casablanca defender Mohamed Oulhaj insists only victory will do when it opens the FIFA Club World Cup on home soil against Auckland City on Wednesday evening (Thursday morning AEDT).