The JRM team said their technical director and team manager was killed on Friday morning.
Kent Police said in a separate statement that a 56-year-old, confirmed by the team to be Stepney, was hit by a truck at 1.28 am after stopping his van on the hard shoulder of the M20 motorway at Ashford.
"For reasons yet to be established, the man appears to have entered the carriageway and was then in collision with an articulated goods vehicle. He was pronounced deceased at the scene," the police said.
McLaren were fined a record $100 million by the International Automobile Federation and stripped of all their constructors' points in 2007 after being found guilty of possessing a 780-page dossier of Ferrari data.
Stepney and McLaren's then-chief designer Mike Coughlan, who had the information at his home, were sacked by their teams.
The FIA took no formal action against Stepney, since he was not a licence holder of the governing body, but recommended that teams should have no professional ties with him for two years.
He never worked in Formula One again.
Ferrari had also accused their employee of attempted sabotage, allegations Stepney denied. The team had claimed a mysterious powder was found around the fuel caps of both their cars before the 2007 Monaco Grand Prix.
Powder turned up in Stepney's trouser pocket but the Briton said he was set up.
In 2010, an Italian court sentenced Stepney to a 20 months in jail, as well as a 600 euro fine, but a plea bargain meant he did not have to serve any time.
Before the 'Spygate' affair, one of the biggest scandals to hit Formula One in the modern era, Stepney had an impressive Formula One resume.
He had worked with Brazilian Ayrton Senna at Lotus and was at Ferrari when Michael Schumacher won five world championships in a row between 2000 and 2004.