The 48-year-old man, locally known as 'Gica' although his real name was Gheorge Hortolomei-Lupu, was found dead in a park in the town of Huskvarna, near Jönköping, earlier this month.
After a post-mortem examination, police launched a murder probe a week after his death. Videos of the teenagers beating and harassing the man were reportedly circulated on social media.
Earlier this week police arrested a 16-year-old Swedish national, who lives in Huskvarna. He denies the allegations, his lawyer said.
The other boy, who is too young to face criminal charges, is also suspected of murdering the man.
Another two boys, also aged under 15, have also been questioned by police. They are suspected of having assaulted or harassed the victim before his death, Swedish media report.
"We have an idea of what happened," police investigator Stefan Sundling told SVT.
Gica came to Sweden roughly four years ago from a town near Bacau in Romania, according to people who knew him. He reportedly lost his job at a printing company and got divorced shortly thereafter. He left Romania and spent time in several other EU countries before settling in Sweden.
He worked in the Jönköping-Huskvarna area as a fruit picker for a while before becoming a bottle collector and full-time beggar. He was involved in Christian local aid group Kyrkhjälpen's efforts to help other homeless EU migrants in Sweden, but his health had taken a serious turn in recent months.
His friends remembered him this week as a man who was "friendly, grateful and kind".