Mr Kaczynski was sworn in by his identical twin brother, President Lech Kaczynski, making Poland the world's only country to have twins in its top two executive posts.
Veterans of the anti-communist Solidarity movement, the Kaczynskis mix conservative social policy and a tough line on corruption with belief in state economic intervention and scepticism of deeper European integration.
Lech Kaczynski said his brother's nomination marked a fresh start for a government often criticised for mishandling relations with its foreign partners and policy drift at home.
"We have to implement plans to build a properly functioning country, without corruption, a country helpful toward its citizens, to build an independent Poland within the EU," President Kaczynski said.
Jaroslaw Kaczynski, the head of the ruling conservative Law and Justice party who had never held public office before, replaced fellow party member Kazimierz Marcinkiewicz, who stepped down last week.
"I want to review the situation, and first and foremost make sure the legislative work moves forward," Mr Kaczynski told a news conference after the first meeting of his cabinet.
"The chief goals of foreign policy are obvious. We are in the EU and are a partner for the US ... but we need to be more decisive and bold in our actions."
Mr Kaczynski kept Mr Marcinkiewicz's team in place, with the exception of bringing in a new finance minister, Stanislaw Kluza, a former bank economist who was also sworn in.
Mr Kaczynski said better use of EU aid and investment in roads and housing necessary to narrow the wealth gap dividing the biggest former-communist EU member with its richer neighbours, would also be high on his government's agenda.
"We must make up the civilisation gap. The only way forward is to build motorways and expressways," he said.
"Plus there is housing. I believe firmly we can build three million flats in the next few years."
The new cabinet is expected to win majority backing in a confidence vote in parliament scheduled for Wednesday.