Ashley Pace had been charged with murdering Jagdev Lally in Smethwick but this week pleaded guilty to his manslaughter.
Mr Lally, who had lived in the Smethwick area but was thought to be homeless at the time of the attack, died two weeks after being assaulted by Pace in the early hours of April 14.
He had been resting next to Pace's partner on bedding in an alley just off the High Street when Pace arrived and attacked him in a jealous rage at around 3am, West Midlands Police said.
Pace, aged 35, punched and kicked Mr Lally as he lay on the floor, leaving him with serious injuries to his head and face.
The 38-year-old was was rushed to hospital with a bleed on the brain after being found by a passer-by around six hours later but died on May 1.
CCTV captured the attack near Tollgate Shopping Centre and Pace, of no fixed address, was initially charged with wounding.
He was charged with murder after Mr Lally's death and was due to stand trial at Wolverhampton Crown Court next week.
However on Thursday Pace offered a guilty plea to manslaughter, which was accepted at the same court.
Mr Lally’s family have since paid tribute to him, saying: “Jagdev was a loving father, son and brother.
“He was the sole provider for this parents in India, who are now totally lost without him.
“They, his son or sisters will never see him again.
“We need answers as to why someone would carry out this attack. We hope justice is served on the assailant so he realises what pain he has caused Jagdev and his family.
“To be taken at such a young age is difficult enough, but for it to be under such tragic circumstances is heart-breaking.”
Detective Inspector Jackie Nicholson, from West Midlands Police CID, said: “This was a vicious and unprovoked attack on a vulnerable man by someone who was simply not happy about where he had laid down to sleep.
“He was left with serious injuries after collapsing and never regained consciousness.
“I’d like to thank the member of the public who helped him and made sure he got to hospital. Sadly, he didn’t survive.
“Nothing will bring Mr Lally back to his family but I hope that seeing the person who caused this unexplainable pain being brought to justice is something that can offer them at least some comfort.”
Pace will be sentenced on January 15 at Wolverhampton Crown Court.