The investigation will determine whether any transactions relating to the works should have been reported, and if so whether it was reported as required.
Johnson has a taxpayer-funded $42,000 allowance for maintaining and furnishing his official residence each year. UK newspaper reports suggests that the transformation of the flat may have cost as much as $280,000.
Ministers have said Johnson has paid for the work himself, but it is unclear whether the refurbishment was initially financed by a loan of some kind, which Johnson is thought to have been required to declare.
The opposition Labour Party has been pressing Johnson on the issue, asking for the head of the UK's civil service investigate.
Labour leader Keir Starmer raised the issue at the weekly Prime Minister's Questions session on Wednesday, demanding to know who had initially paid for the home improvement project.
In response, Johnson said: "The answer is I have covered the costs."
He added: "I have conformed in full with the code of conduct and the ministerial code and officials have been advising me throughout this whole thing."
Asked last month about the refurbishment, Johnson's spokeswoman said all donations, gifts and benefits were properly declared, and that no Conservative Party funds were being used to pay for the refurbishment.
The prime minister's former chief advisor, Dominic Cummings, who has fallen out with Johnson, said he had told his then-boss last year that alleged plans to ask donors to pay for the renovation secretly were "unethical, foolish, possibly illegal."