The move – which came moments before a Keir Starmer speech attacking the prime minister’s refusal to act – follows a week of No 10 declining to say if he backed the crackdown.
In a letter to the Commons Speaker, Mr Johnson also proposed that the code of conduct for MPs should be updated.
He also said he wanted a situation where “MPs who are prioritising outside interests over their constituents are investigated and appropriately punished”.
It comes two weeks after Mr Johnson himself tried to rip up Commons sleaze rules – to protect Owen Paterson from punishment – before being forced into a humiliating retreat.
At his press conference, Keir Starmer hailed “a very significant victory for the Labour party”, which would not have happened if it hadn’t “forced that vote”, to be staged on Wednesday.
The vote was set to challenge Conservatives MPs to outlaw second jobs – potentially forcing the prime minister into the embarrassing position of whipping them to oppose it.
However, Mr Johnson’s climbdown did not appear to go as far as Labour’s position – a ban on second jobs, except in the public sector – suggesting a Commons clash still looms.
Labour is also demanding the release of all the minutes of meetings between the government and Randox, which employed ex-minister Mr Paterson as a consultant.
In his letter to the Speaker, Lindsay Hoyle, Mr Johnson said it was vital to protect the Commons “reputation” by “ensuring the rules which apply to MPs are up to date, effective and appropriately rigorous”.
He said he was “a matter of regret” that the Commons had not adopted a watchdog’s recommendations, three years ago, of a tougher code of conduct – although the government is not believed to argued for them.
Backing the changes now, the prime minister pointed out they would ensure that any MP’s outside role would “be within reasonable limits and should not present them from fully carrying out their range of duties”.
They would ban “any paid work to provide services as a parliamentary strategist, adviser or consultant, for example, advising on parliamentary affairs or on how to influence parliament and its members”.
The beefed-up code should state: “MPs should never accept any payment or offers of employment to act as political or parliamentary consultants or advisers.”
Labour MPs were quick to ridicule Mr Johnson proposing the crackdown, Wes Streeting, the shadow child poverty secretary, tweeted: “Arsonist calls for fire to be put out.”
And Catherine West, the shadow Europe minister, said: “Two weeks ago Boris Johnson and his MPs voted to protect an MP who broke the rules. The proposals he’s been forced to make today are welcome, but they don’t go far enough.”