He managed Egypt between 1985 and 1988, before he returned to coach Wales for a second stint in 1994.
Smith's coaching spell started when he was first appointed as Director of Coaching of the Football Association of Wales then he succeeded Dave Bowen as the Welsh national team coach in 1974.
One of his achievements was guiding Wales to the quarter-finals of the 1976 European Championships.
Former Swansea City striker Alan Curtis - who played his maiden international game for Wales under Smith in 1976 - joined the Welsh FA in mourning the departed legend.
"I've always said that Mike was the first proper coach that I'd ever worked with in terms of the way he spoke about the game, his ideas on the game," Curtis told