Jeremy Corbyn insisted his “voice will not be stilled” and promised to keep demanding justice for the country in his final Prime Minister’s Questions appearance.
Mr Corbyn is due to step down as the Labour Party leader next month.
Mr Johnson said: “Perhaps I could begin by pointing out that this is the honourable gentleman’s last Prime Minister’s Questions and it would be appropriate for me to pay tribute to him, his service to the party and indeed the country over the last four years in a very difficult job.
“We may not agree on everything but no one can doubt his sincerity and determination to build a better society.”
The Conservative Party leader also thanked Mr Corbyn and opposition MPs for working across party lines on the coronavirus crisis.
Mr Corbyn said in reply: “I thank the Prime Minister for his very kind remarks. He was talking as if it was some kind of obituary.
“To let him know, my voice will not be stilled, I will be around, I will be campaigning, I will be arguing and demanding justice for the people of this country and indeed the rest of the world.”
The two leaders clashed over the government’s response to the coronavirus outbreak with Mr Corbyn calling on the Prime Minister to clarify when NHS staff would receive the vital protective equipment they need to treat patients with Covid-19.
He claimed the Health Care Supply Association had been forced to use Twitter to ask DIY shops to donate protective equipment to NHS staff.
“This is an appalling situation,” said Mr Corbyn.
“When will NHS staff, social care staff and community nurses and all other staff relating to healthcare get the PPE equipment they absolutely desperately need?”
The Prime Minister responded by saying that the Army had distributed 7.5million pieces of equipment in the last 24 hours.
When asked what protection private renters would receive from eviction, Mr Johnson said the government has “gone further” to offer protection to renters.
Mr Johnson told MPs: “We’re also making sure that no-fault evictions are no longer legal and that is part of the Bill.”
Mr Corbyn added: “We need clarity not confusion, we need delivery not dither.
“This crisis shows us how deeply we depend on each other.
“We will only come through this as a society through a huge collective effort.”
Mr Corbyn resigned as Labour leader in December after his party suffered a major defeat by the Tories in the winter general election.