Nicola Ford, of Kirkstall, has named the man as Lee Jenkins - whom she was in a relationship with for five years.
READ: Councils must publish plans to tackle homelessness, government demandsHe was a long-term rough sleeper and died in hospital in Leeds last Saturday.
Although they were no longer together at the time of Lee's death, they remained on friendly terms and she had recently offered him a place to stay.
Lee was fond of Nicola's daughters, who are now in their teens, and they called him 'Dad'.
They are pictured together above at a park in Beeston around six years ago. The tragic stories behind recent rough sleeper deaths in Leeds
"Lee was my boyfriend of nearly five years a while ago now, but my kids saw him as Dad and he always kept in touch. He sent cards and money when he could.
"It's devastating news. He was such a kind man. Even though he had nothing he'd always do anything for anyone. His dog Lady was his best friend and he fed her before himself. We tried to get him onto our sofa but he's such a proud man.
READ: Shock and sadness as tributes are paid to homeless man who died in Leeds"He was the closest thing to a father figure my daughters ever had."
Nicola and her daughters are now hoping to volunteer for a homeless charity in Lee's memory and are also planning to release balloons as a tribute to him.
Lee was well-known and popular among members of the street community, including volunteers from outreach charity Simon on the Streets who regularly worked with him.