The government has announced a review covering David Cameron’s efforts to lobby ministers on behalf of finance firm Greensill Capital.
The former prime minister has been criticised for contacting ministers via text on behalf of the company, which collapsed in March.
Downing Street said the probe would be led by lawyer Nigel Boardman on behalf of the Cabinet Office.
Mr Cameron has said he has not broken any codes of conduct or lobbying rules.
But in a statement on Sunday weeks after reports of his lobbying emerged, the former Tory leader said that he should have contacted ministers through “formal” channels.
A spokesman for the former PM told the BBC: “David Cameron welcomes the inquiry and will be glad to take part.”
Mr Cameron began working as an adviser to Greensill Capital in August 2018, two years after he stepped down as prime minister.
In recent weeks, newspaper reports have revealed he texted Chancellor Rishi Sunak and other Treasury ministers on behalf of the company.
Mr Cameron said he had been trying to involve the company in a government-backed emergency loans scheme for firms hit by the Covid pandemic.
The government went on to reject his plans to involve Greensill in the so-called Covid Corporate Financing Facility.
It has also been revealed that Mr Cameron met Health Secretary Matt Hancock for a “private drink” in 2019 to discuss a payment scheme for the NHS.
An ally of Mr Hancock said he had “acted in entirely the correct way”.
The PM’s official spokesman said the review would examine the awarding of contracts for supply chain finance, a financial technique in which Greensill specialised.
“This independent review will also look at how contracts were secured and how business representatives engaged with government,” added the spokesman.
“There is significant interest in this matter, so the prime minister has called for the review to ensure government is completely transparent about such activities”.
Mr Boardman, a non-executive board member at the government’s department for business, will be expected to report “promptly,” he added.
Speaking after reports of an inquiry emerged but before Mr Boardman’s appointment was confirmed, Labour’s Rachel Reeves said: “This has all the hallmarks of another cover-up by the Conservatives.”
“This is another Conservative government attempt to push bad behaviour into the long grass,” she added.
She called for Mr Cameron, Mr Sunak and Mr Hancock to answer questions in Parliament about the matter, adding: “we need answers on Greensill now”.
Mr Cameron’s predecessor at No 10, Gordon Brown, welcomed an inquiry, adding: “it’s important to get to the bottom of this”.
The ex-Labour leader told BBC News: “I don’t really think former ministers and prime ministers should be engaged in lobbying for particular commercial companies, when they are lobbying their successors whom they know very well and could have privileged access to.
“Lobbying in this commercial way could also be a stain on our democracy, and therefore an inquiry is completely appropriate.”
Former ministers and senior civil servants are banned from lobbying for two years after they leave government, a rule Mr Cameron followed.
Mr Brown had suggested earlier on Monday the ban should be extended to five years if existing rules prove inadequate.