"I am pleased that we have achieved this historic transfer because bringing Mitrovic to Anderlecht was a priority for our sports department," Anderlecht general manager Herman Van Holsbeeck told the club's official website.
"The fans can look forward to the arrival of a talented young striker who already has some international experience at his club as well as with the national team," he said.
The robust teenager, who has made one international appearance at senior level, was a key player in Serbia's shock triumph at this month's U19 European championship in Lithuania.
He also scored some crucial goals in his first professional season with Partizan last term, when the club clinched a record sixth successive league title and their 25th overall.
Partizan's board was divided over Mitrovic's departure and one of its senior members resigned earlier on Monday after a majority voted in favour of the move, which should ease the club's financial woes.
"The club respects the wish of Mitrovic and his family to continue his career abroad and we thank him for his time here," Partizan said on their official website).
Anderlecht, who also signed Serbia midfielder Luka Milivojevic from Red Star Belgrade in July, will play in this season's Champions League group stage while Partizan face Swiss rivals Thun on August 22 and 29 for a berth in the second-tier Europa League.