Jarvis senior independent director Steven Norris said: "Although these appointments have been made in special and sad circumstances, they are part of the normal and planned management transition in the group."
Moayedi has been chief executive of Jarvis since 1994. Hyde joined the board in December 2000 and was appointed chief operating officer in August 2001.
Jarvis intends to appoint three non-executive directors, and has hired headhunters to begin the search. The company has six executive and three non-executive directors, but wants a better balance. The paucity of non-executive directors was highlighted earlier this year by the resignation of non-executive Sherry Coutu, who wished to spend more time with her family.
The contractor's preliminary results for the year to 31 March will be released on 12 June.