The Yorkshire tourism body – whose chief executive paid back a reported £40,000 in apparently misclaimed expenses after his abrupt departure – has agreed to let investigators examine all expense claims over the past six years.

Welcome To Yorkshire’s former boss Sir Gary Verity resigned suddenly in March after an internal investigation into his expenses, which included claims related to his sister’s funeral earlier this year.

The organisation, under pressure from local councils who have contributed much of the £14.9m in public money it has received since 2013, has commissioned forensic accountants BDO to examine all expense claims made by Verity and other members of the senior management team and board.

That should include everything Verity claimed in his successful bid to woo the French organisers of the Tour de France, who agreed to stage the start of 2014’s race in Yorkshire.

Christian Prudhomme, the French race director, has defended Verity, saying: “I cannot help but feel sad for the man who made me discover your beautiful county, for the man who brought together our ‘ooh la la’ with your ‘ee bah gum’, the man who made me love Yorkshire: mon ami, Gary Verity.”

The law firm Clarion will conduct a separate inquiry into the culture, governance, procedures and management at WTY after allegations of bullying by Verity.

WTY has not committed to publishing the expenses but instead said a report “outlining the key themes, findings and recommendations” would be made publicly available when the investigations were completed, by the end of June.

Verity was knighted the year after the Yorkshire Grand Départ in 2015 and last year was appointed deputy lieutenant of West Yorkshire, making him an official representative of the Queen in what he always called “God’s own county”.

WTY’s chair, Ron McMillan, who announced the expenses investigation ahead of the Easter weekend, has also confirmed he would be stepping down.

McMillan, a former partner at the accounting firm PWC, said he would quit after it became clear that Yorkshire local authorities, who provide the bulk of WTY’s funding, were “looking for a significantly revamped board to take the business forward.”

He had been criticised for a statement released on Verity’s departure in which he brushed over the affair, saying it was “very much business as usual” and that the board didn’t believe Verity had committed any criminal offence.

In his parting statement, McMillan said WTY should be judged on the benefits it brought to the Yorkshire economy rather than how it spent its own money. He said: “I hope Welcome To Yorkshire will continue to be a highly commercial organisation which recognises that outputs in the form of economic growth are more important than inputs.

“In particular, I hope it will expand its range of activities on an international stage and that it will be allowed to invest in all of the things that are important to its success; business development, building relationships, getting out and about and attending events, engaging sponsors and influencers (current and prospective) and pursuing new sources of funding to name a few.”

Keith Stewart has been named interim chair and immediately announced the organisation would become more open. He said: “In the interests of greater transparency, we will start by making all appropriate board meeting documents public in future, including agendas, papers and minutes.”