The man turned himself into police directly after the killings, telling police officers "I have killed five people".
The victims are believed to be the man's ex-girlfriend (19), new boyfriend (25), her brother (25), mother (51) and father (59).
Police told Austrian media that there had been a dispute between the man and his new girlfriend at a local restaurant the previous evening, with the relationship between having ended two months ago.
The man approached the family home at 4am on Sunday morning - where he had previously lived with the woman and her family - before being told by the victim's father that the relationship was over, before being told to leave the house.
He is reported to have driven home and taken a gun from his brother, before returning to the house at approximately 6am, entering the house by breaking a window.
He climbed a balcony to reach his ex-girlfriend and her new boyfriend, who were sleeping in a locked apartment inside the house.
Police said that the crime appears to be motivated by jealousy at the "end of a love affair", also telling local media that the weapon was licensed and kept in a locked safe.
Kitzbuehel Mayor Klaus Winkler said that it was a dark day for the holiday town.
"There has never been such an event in this form (in Kitzbuehel). It is a tragedy and we are all deeply shocked," he said.
"This was a completely irrational act... a terrible family tragedy".