The young man also confessed to several other cases of cruelty to animals when handed himself over to police in Lerum, a town outside Gothenburg in southwestern Sweden. He is currently under medical observation.
"My client is responsive but he's in a very bad condition," lawyer Göran Franzén told the TT news agency.
Prior to revealing his identity, the perpetrator had claimed responsibility for some twenty cases of cruelty to animals in an anonymous note posted alongside the dead cat on the police station door.
Cats were the focus of a number of his attacks. One dead cat was pushed through a letter box, while another was hung by a measuring tape from a door handle at the local district court. He also tortured a dog by cutting off its tail and ears.
Police had already isolated the 20-year-old as one of their main suspects following several leads from members of the public. He was taken in for questioning in connection with a wave of attacks on animals in Lerum but was later released.
On Tuesday morning the 20-year-old contacted police and confessed to the attacks, which have upset animal lovers across Sweden.
In a statement issued by the police, the man's family have asked to be left alone.
"The family have been living under an awful lot of pressure," said Franzén.
"I don't want to speculate on the nature of the illness, or the reason he has given for torturing the animals. But he is being attended to by doctors while he is being detained."
The 20-year-old is expected to be remanded in custody. Franzén said he did not wish to speculate on any eventual custodial consequences for his client.
"It's too early to say. Indictments for cruelty to animals are unusual, and are generally related to cases of neglect in the care of animals. The issue of whether my client will be sentenced to prison or institutional care is something everyone realises will come up during the trial," said Franzén.