"The president of the republic of Poland, Lech Kaczynski, has designated Jaroslaw Kaczynski as prime minister," the presidency said in a statement.
The widely expected announcement came shortly after outgoing Prime Minister Kazimierz Marcinkiewicz submitted his resignation and it was accepted by President Kaczynski.
Mr Marcinkiewicz's resignation at the head of Poland's coalition government means his whole cabinet automatically quits.
Mr Marcinkiewicz, who made the surprise announcement on Friday that he was standing down, just nine months after being nominated for premier – by Jaroslaw Kaczynski, as party leader - will head the government until a new cabinet is appointed.
Jaroslaw Kaczynski, the head of the ruling conservative Law and Justice (PiS) party, now has two weeks to name a new cabinet and an agenda for governing Poland.
He will present both to lawmakers, who will then have a further two weeks to approve his nomination as premier and his proposed government programme.
Jaroslaw Kaczynski has said that his new government will be the same as that of Mr Marcinkiewicz, apart from a new finance minister.
If Jaroslaw Kaczynski, 57, is confirmed by parliament in the post, he will be breaking a vow he made during his brother Lech's successful presidential election campaign last year.
Mr Jaroslaw said then that he would not take up the post of prime minister if Lech were elected president, because neither the Polish people nor Poland's international partners would tolerate a fraternal double act in the two key positions of Polish politics.