Amanda Spielman, who co-founded the ARK academy chain after a 22-year career in corporate finance, has been recommended by Education Secretary Nicky Morgan as her preferred candidate for the role.
If confirmed in post, Spielman will be tasked with overseeing scrutiny of schools and children's services across England, as well as driving through inspections reforms outlined in the government's recent education white paper.
She has been chair of Ofqual since 2011.
Morgan said: "From helping to set up one of the country's top academy chains, to acting as a council member for the Institute of Education, to overseeing our ambitious qualification reform programme, Amanda has extensive experience at the frontline of the education system, making her uniquely qualified to take up this important role.
"I know that she is the right person to deliver the education white paper's commitment to continue to improve the quality and consistency of Ofsted's inspections ensuring that it plays a central role in realising our vision of educational excellence everywhere."
Prior to helping set up ARK in 2005, Spielman worked in corporate finance, holding roles at KPMG and Kleinwort Benson.
Before being appointed Spielman needs to meet with the House of Commons education select committee and be approved by the Privy Council.
In February, it was reported that Morgan was considering candidates from the US, including the head of New York City's education watchdog, to replace Wilshaw, who completes his five year term in December.
Kevin Courtney, acting general secretary of the National Union of Teachers, said: "To have as the new chief inspector of Ofsted a person who has no teaching experience and who is heavily implicated in the academy programme certainly does call into question both their suitability and impartiality for the job.
"It is a sad indictment of this government's attitude to education that they place such little value on the experience of teachers and head teachers that they would not consider such a background necessary for the chief inspector's role."
The Educational Excellence Everywhere White Paper, has been marred by controversy since it was published in March. Last month, Morgan was forced to backtrack on plans to force all schools to become academies by 2022, following criticism from Conservative MPs and education experts.