The news was announced at a press conference on Sunday, presided over by Kosiniak-Kamysz himself.
But Kosiniak-Kamysz said that if someone “more worthy of honour” was put forward by an alliance of Polish opposition parties he was prepared to stand down.
Donald Tusk, former leader of Civic Platform, which is Poland's largest opposition party, has not yet announced whether he will return to Polish politics and run for president in 2020.
Tusk was the prime minister of Poland from 2007 to 2014, when he resigned to become president of the European Council, a key European Union leadership position.
His term in Brussels ends on November 30.
Meanwhile, Poland’s ruling conservatives have reaffirmed their support for incumbent President Andrzej Duda, who is expected to seek re-election in May.