Steven Gallant, 42, told how he started to tackle Usman Khan armed only with a chair during the attack which began at a nearby prisoner rehabilitation event.
Gallant, who was out on licence to attend the event, is serving a minimum of 17 years for killing ex-firefighter Barrie Jackson in Hull, 15 years ago.
Khan, who killed Saskia Jones and Jack Merritt, was later shot dead by police.
Three others were injured in the attack which began at Fishmongers' Hall on November 29.
Gallant is the last of three people who were filmed restraining Khan on the bridge to be identified.
In his first interview since what he called "that tragic day", Gallant said he went to investigate after he heard noises from a lower floor of the building.
"I could tell something was wrong and had to help," he told PA news agency.
"I saw injured people. Khan was stood in the foyer with two large knives in his hands."
"He was a clear danger to all, so I didn't hesitate."
Last month, civil servant Darryn Frost described how a man - now identified as Gallant - used a wooden chair to keep the knifeman at bay, before throwing it at Khan when he revealed his suicide belt, which was later shown to be fake.
Mr Frost said he then handed Gallant a narwhal tusk, which he had found on a nearby wall display, as Khan "started running towards him (Gallant) with knives raised above his head".
Gallant has offered "special thanks" to Mr Frost. "Had he not passed me the narwhal tusk at that crucial moment, not only could I have been killed, the situation could have been even worse," he said.
He also described reformed ex-prisoner John Crilly, who used a fire extinguisher to help subdue Khan, and a chef - known only as Lukasz - who was stabbed five times when he stepped in to help, as "extremely brave".
Gallant was jailed, alongside his accomplice James Gilligan, in 2005 for carrying out a fatal attack on 33-year-old former firefighter Mr Jackson.
During their trial, Hull Crown Court heard the attack was carried out because Gallant wrongly believed Mr Jackson had attacked his girlfriend.
"Nobody has the right to take another's life and I offer my sincere apologies to my victim's family for the hurt caused," Gallant said.
"I can never bring that life back, and it is right that I was handed a severe penalty for my actions.
"Once I'd accepted my punishment, I decided to seek help.
"When you go to prison, you lose control of your life. Your own future relies on the decisions of others.
"Bettering yourself becomes one of the few things you can do while reducing the existing burden on society."
Since going to prison, Gallant, who will be eligible for parole in 2022 subject to approval, has "vowed never to turn to violence again".
He has since learned to read and write, is studying for a business studies degree and was taking part in the Learning Together rehabilitation project, which was hosting the event at which Khan struck.
He said the deaths of course co-ordinators Mr Merritt, who he met in 2016, and Miss Jones were an "unbearable blow" and the "sense of loss is immense".
Gallant described Mr Merritt as a "role model and friend".
He said: "Jack didn't care who you were: he cared about you and your future; he saw who you could become and did not define you by your past. I will miss him badly."
Miss Jones, he said, was "highly respected and loved" by those involved with the course.
He added that he was "certain" the pair would wish for the Learning Together programme to continue.