Grezegorz Kowalczyk, 41, was told he must serve a minimum of 16 years in prison after he was found guilty of murdering fellow Polish national Waldek Mural, 57, in Burley Park.
Mr Mural was found with horrific injuries to his head, face and body on the morning of September 5 last year.
He had suffered 11 rib fractures, a fractured sternum, a punctured lung and a tear to a neck artery.
The jury at Leeds Crown Court heard the motive for the attack was still unclear. The two men had met for the first time the previous evening.
CCTV showed them together on Armley Town Street and buying beer in a shop before heading into the park at 10.13pm.
Footage then showed Kowalczyk walking alone along Cardigan Lane at 10.44pm.
He was filmed going into a Co-Op store and buying lager and a bottle of water. Kowalczyk then used the bottle of water to wash his hands.
Cameras captured him returning to his home on Pavilion Mews, Headingley.
He was filmed in the hallway removing his shoes and socks and rolling up the bottom of his trousers before walking up the stairs.
Mr Mural’s mobile phone was found on him and the last call made from it was 9.50pm.
Kowalczyk spoke to other members of the Polish community who noticed he had swollen hands.
He gave various accounts to people about how this had happened. He told one person that he had been sleeping on a bench and had punched someone who “got in his face.”
He told another person he had had a fight in a park.
The prosecution told the jury there was no DNA evidence linking him to the killing but claimed Kowalczyk had been “forensically aware”.
He has a previous conviction for robbery in his home country in 1993.
The court heard Kowalczyk had come to Poland in 2014 on the promise of work despite not having a passport.
His barrister, Peter Moulson, QC, said the promise of work had fallen through and he had survived by visiting soup kitchens and rummaging through bins.
Sentencing Kowalczyk, Mr Justice Edis said: “Something happened in the park which made you lose your temper with him and you subjected him to a brief but ferocious assault.
“No weapons were used but you punched him to the ground and stamped on his neck and then stamped on his back.
“You immediately decided to try to get away with what you had done and did not try to get him any help, You left him for dead and abandoned him to his fate.
“Essentially you attacked a defenceless man. He was older then you, smaller than you and far more drunk than you were.
“He was incapable of lifting a finger to save himself.”
Temporary Detective Superintendent Jim Dunkerley, of West Yorkshire Police Homicide and Major Enquiry Team, said: “Kowalczyk murdered Waldek Mural for no apparent reason after the two men met in the street only a short time beforehand.
“As far as we can establish, they were not known to each other prior to the incident.
“Kowalczyk has a previous conviction in Poland for a violent robbery and we can only speculate that may have been the motive.
“To have taken a life in such sudden and violent circumstances clearly shows him to be a dangerous individual. We hope Mr Mural’s family in Poland can find some consolation in knowing that he has now been brought to justice.”