They were his father, 53, his mother, 52, and his sister, 21.
Police also confirmed that three people found dead at the gunman’s home after the attack were members of his family.
He was taken to hospital with injuries from the shootout and later died there, the Polish authorities confirmed.
Police opened a terrorism investigation after the attack in the heart of the old town.
A 24-year-old Polish man who opened fire in a market square in Kraków has died in hospital after being wounded in a shootout with police, authorities said. Wearing military-style clothing and a bulletproof vest, the gunman drove at high speed into the square, which is usually packed with tourists, and began shooting at random, Kraków police spokesperson Katarzyna Cisło said.
The confirmation came in an update on the morning after the shooting, as Poland observed the first of two days of national mourning declared after the rare mass shooting.
Police said the suspect had no criminal record and held a firearms licence. He initially kept firing even after officers wounded him during the exchange of fire, police said.