Stepney was involved in the 'spygate' scandal, in which he was accused of passing a technical document to McLaren from Ferrari in 2007.
The mechanic, who worked for Lotus and Benetton throughout his career, left Formula 1 after the incident came to light.
Stepney was employed by JRM in 2010 and continued working for them up until his death.
"The rest of the engineering and race team here at JRM learned an unimaginable amount from Nigel in the four short years he was with us and his death this morning has shocked everyone to the core," ESPN quotes owner James Rumsey as saying.
"Today, the motorsport world has lost one of its greatest characters and competitors. He will be sorely missed and we send our sincere condolences to his family and the many friends he leaves behind. Our prayers and thoughts are with Ash and Sabine."
Stepney began his career with Shadow in 1977.