Police had issued a national alarm as they searched for the man, who was arrested on Friday night in the Uppsala region. He was brought to the police station in Karlstad for questioning and admitted to the murder.
The 37-year-old's lawyer was present when the questioning continued on Saturday.
"I can only say that he has confessed...I cannot reveal anything else," lawyer Lennart Jemtelius told news agency TT.
The 27-year-old was reported missing on Monday. He was supposed to go abroad on vacation but failed to reach his destination. According to a post on his Facebook page, he was travelling to Cyprus together with his boyfriend, but police said the couple never left Sweden.
When the man's relatives could not reach him, they contacted the police.
On Friday, flowers, candles and greetings were placed outside the murdered man's home, Swedish Radio's P4 Värmland station reported.
The detention hearings will be held Sunday at the earliest, prosecutor Kurt Runhäll told TT.