David Hart said the Government's schools white paper did not go far enough and without more radical reforms ministers have no chance of raising standards.
Mr Hart, who retired in August as leader of the NAHT after 27 years, told his former union colleagues to stop "whingeing" about new policies. In a speech in London, he said: "We have a number of outstanding school leaders but there are not enough in the system.
"I see no reason why the Government should not explore the possibility of recruiting executives from private and public-sector backgrounds who have not taught but who have what it takes.
"They will need an in-depth induction of, say, a year before appointment, but we should not fight shy of harnessing all the talents in the drive to raise tandards."
Mr Hart told the Foundation and Aided Schools National Association that those who purport to speak for school leaders look "foolish" when they repeatedly "ape Oliver Twist" and ask for more money. Standards will not rise if "union leaders keep whingeing about new policies", he said, adding:
"The white paper is a real opportunity for school leaders to set the agenda."
He said there was no reason why private prep-school teachers were subject specialists but staff in state primaries were not. "Urgent action" was needed to improve the specialist subject knowledge of primary teachers - "otherwise the country does not stand a cat in hell's chance of seeing standards raised to the levels demanded by global competition".
Mick Brookes, now general secretary of the NAHT, described Mr Hart's comments as "an extraordinary statement, particularly coming from an ex-general secretary of a headteacher's association."
The former primary head said: "You need people running schools who understand what it's like to teach. One of my best teachers came from industry, but he trained and qualified and learned his trade as a teacher before becoming an assistant head."