The mother and her nine-month-old baby were found at the bottom of a quarry in Dalby, near Lund, earlier this week. They were rushed to hospital but were unable to survive.
Authorities initially believed the pair had fallen off the nine-metre cliff face, but soon after arrested a 30-year-old man after searching the home of the woman.
Local newspapers reported that the man and woman were in a relationship, and were the parents of the child.
The man confessed to the crime on Thursday night, his lawyer told the TT news agency. The suspect said that it was him who had alerted police.
At a hearing at the Lund district court on Friday morning the man was officially arrested pending trail and is being held on probable cause on suspicion of two murders, according to the court's decision.
He appeared in court with a yellow blanket covering his head for protection. The man will be detained ahead of his trial and will undergo a psychiatric evaluation.
His lawyer Per Schånberg told the local Sydsvenskan newspaper that the suspect had spoken in great detail about what had happened on the night of the incident in Dalby.
"I can't say much more apart from that right now he is a terribly heartbroken man," he said.
It's believed that the man is a member of the military services and returned back to Sweden in 2013 after serving a mission in Afghanistan. His most recent post was with the South Skåne P7 regiment. Local media reported that he has no previous criminal record.
Police investigate the scene of the crime. Photo: TT