The Tory leadership candidate’s views on the formula, which allocates public spending increases to the Scottish Parliament, have been under scrutiny as the race to succeed Theresa May in Number 10 nears its conclusion.
In 2014, a day after the Scottish independence referendum, Mr Johnson indicated that he would be in favour of a redesigned funding model.
The Conservative MP made the comments after the late Labour peer Joel Barnett, who devised the formula, said that it was unfair.
“We can’t just go on with a system that even Joel Barnett himself thinks is outdated,” Mr Johnson said in 2014.
“There’s a good way of honouring this odd promise. Ask Lord Barnett who has disassociated himself from this formula to get on with redesigning it.
“He said, Lord Barnett said himself, it was a crazy and outdated to continue to funnel money in this way.
“If he thinks so then I’m sure everybody else south of the Border thinks so. It’s my solution for honouring what is a slightly reckless promise.”
A spokesman for Jeremy Hunt said: “The Barnett formula is essential to protect Scotland’s public services. That’s why a government run by Jeremy would maintain it, to help ensure Scotland’s schools and hospitals get the funding they need.”
Scottish Conservative MP John Lamont, campaign manager in Scotland and one of Jeremy Hunt’s original backers in his bid to become prime minister, said that it would be “reckless” to scrap the formula.
He said: “Boris is already refusing to debate Jeremy. He shouldn’t dodge questions on the Barnett formula too.
“This shouldn’t even be a difficult question. There is no case for scrapping the Barnett formula. The only other people who want to get rid of it are the SNP by dividing the UK.
“Boris said it was reckless of David Cameron to commit to keeping the Barnett formula. The only thing reckless would be scrapping it.”
He added: “By suggesting he would scrap Barnett, Boris is handing a gift to the SNP. This is yet another reason that Jeremy is the prime minister that Nicola Sturgeon doesn’t want.
“Boris should U-turn immediately and follow Jeremy in pledging to keep the Barnett formula. That is what’s best for Scotland and the Union.”
SNP MSP Tom Arthur suggested that scrapping the formula would “slaughter” public services in Scotland.
Mr Arthur said: “It is outrageous that the Tories are now plotting to use Brexit as an opportunity to railroad systematic cuts to Scotland’s budget - offering a grim insight into what Scotland can expect from the next Tory prime minister.
“The Tories have longed for the opportunity to hammer Scotland’s budget for years - but the people of Scotland won’t stand by while Westminster politicians plot to cut money from our vital public services to fund their disastrous no-deal Brexit.
“Yet again the mask has slipped and fatally undermined the Tories’ attempts to portray themselves as working in Scotland’s best interests.”
Mr Arthur continued: “Boris Johnson’s latest scheme to appoint the next Tory leader as Minister of the Union is simply laughable - voters will see this meaningless gimmick for what it is.
“With the hard right-wing of the Tory party threatening to axe the Barnett formula and slaughter Scotland’s public services it’s time to take our future into our own hands.
“More and more voters are ready to choose a different path to secure a brighter vision for a better Scotland.”