Sexton, OBE, led England U21s to two European trophies during the 1980s and also had spells in charge of QPR and Coventry.
Sexton was appointed the first technical director at the FA national school at Lilleshall where he mentored the likes of Paul Gascoigne, Sol Campbell, Glenn Hoddle, Michael Owen and Alan Shearer.
FA chairman David Bernstein said: "The whole of The FA is saddened by this news.
"Dave Sexton was synonymous with English coaching and was one of those people that sat right at the heart of our organisation during his time with us.
"He had many friends at the FA including Roy Hodgson and former England managers such as Sven-Goran Eriksson and Terry Venables whom he worked alongside.
"His achievements speak volumes, but his success with the England Under-21 sides of 1982 and 1984 are something that will always be remembered with great fondness.
"Our thoughts are, of course, with Dave's family at this difficult time."