The concession came ahead of a Commons debate and vote on releasing details of the work secured by the firm which employed the disgraced former cabinet minister as a consultant.
Keir Starmer, who is pushing for the lid to be lifted, told the prime minister: “We’ll take that.”
The climbdown – which follows Mr Johnson’s U-turn over banning MPs’ having consultancy jobs – came in a stormy prime minister’s questions which saw him repeatedly rebuked by the Commons speaker.
Lindsay Hoyle told him to “sit down” – as he tried to ask questions of the Labour leader – saying “You may be the prime minister of this country, but in this House I’m in charge.”
Mr Johnson again refused to apologise for the botched handling of the Paterson scandal, leading Sir Keir to brand him “a coward”.
On the Randox contracts, the Labour leader said: “We know that he sat in on a call between Randox and the minister responsible for handling health contracts.
“We know that Randox has been awarded government contracts worth almost £600m without competition or tender.”
Sir Keir said the “only one way to get to the bottom” of the affair was to release the contracts, asking: “Will he vote for it? Or will he vote for another cover up?”
In response, Mr Johnson said: “I’m very happy to publish all the details of the Randox contracts, which have been investigated by the National Audit Office already.”
Sir Keir was then rebuked for using the word “coward” and told the Speaker: “I withdraw it – but he’s no leader.”
Later, his spokesperson questioned whether all the “minutes” of conversations would be released, as Labour is demanding, saying: “Let’s see what the prime minister has actually agreed to release.”
Put on the back foot again over sleaze, Mr Johnson was taunted that he “somehow expects us to believe he’s the man to clean up Westminster”.
Sir Keir added: “He led his troops through the sewers to cover up corruption and he can’t even say sorry. The truth is that beneath the bluster he still thinks it’s one rule for him and another for his mates.”
The prime minister tried to turn the tables by alleging “Mish-conduct” by the Labour leader, who did paid work, as an MP, for the top law firm Mishcon de Reya.
“We will get on, on a cross-party basis, with taking forward the business I have outlined and we will get on with the business of this government,” he told MPs.
He told the SNP leader, Ian Blackford: “I think these constant attacks on the UK’s levels of corruption and sleaze do a massive disservice to billions of people around the world who genuinely suffer from governments that are corrupt and genuinely have no ability to scrutinise their MPs.
“This is one of the cleanest democracies in the world and people should be proud of that.”
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