Kieran Gillespie, 26, stabbed Leon Barrett-Hazle while travelling through Handsworth, Birmingham, on 23 January.
Gillespie, from Wellesbourne Road, Handsworth, denied murder claiming he had acted in self-defence but Mr Barrett-Hazle was unarmed.
The judge at Birmingham Crown Court said Gillespie must serve at least 26 years in prison.
Gillespie boarded the number 11A bus and took a seat near the victim, the trial heard.
Following a short argument, Gillespie stabbed Mr Barrett-Hazle multiple times before walking off the bus.
While passengers were attending to Mr Barrett-Hazle, Gillespie returned to retrieve a baseball cap before walking away once more.
Mr Barrett-Hazle, 35, was stabbed fatally in his neck, a post mortem revealed.
The attack was captured on CCTV and Gillespie handed himself in two days later, West Midlands Police said.
Det Insp Warren Hines said: "This was a completely mindless killing of a man who had done nothing out of the ordinary.
"The ferocity of the attack coupled with Gillespie's nonchalant actions in the immediate aftermath were particularly troubling aspects of this case.
"My abiding hope is that Leon's family find some small comfort in today's conviction."
Georgina Davies, senior crown prosecutor, said Gillespie's attack had been "unprovoked and frenzied".
The family of Mr Barrett-Hazle, who was from Smethwick in the West Midlands, paid tribute to him, saying they had been left devastated by the loss of a "wonderful, warm, kind, generous of heart and much loved" family man.
A man has been jailed for life for murdering a stranger on a bus after a row on the top deck.