In the meantime, assistant coach Stephen Frail will assume the role of "caretaker manager" and will be given full control over first-team affairs, including player selection.
Ambiguity has long surrounded responsibility for picking the team with Frail admitting in the past to having little input in the process.
The new man will be assisted by both Frail and sport director Anatoly Korobochka and will ideally boast experience of management in the British game.
John Robertson, George Burley, Graham Rix and Valdas Ivanauskas have all been and gone since the arrival of majority shareholder Vladimir Romanov.
A statement from the club said: "The board of Heart of Midlothian Football Club has begun the search for a football manager to fill the current vacant post at Tynecastle.
"The manager, who will have full responsibility for team selection, will be an experienced football manager and will preferably have experience of management in British football.
"The new manager will work with sport director Anatoly Korobochka and Assistant head coach Stephen Frail.
"In the interim Stephen Frail will assume the 'caretaker manager' role at Hearts with full responsibility for team selection and coaching of the first team squad."
A dismal run of form has resulted in Hearts slumping to 10th in the Clydesdale Bank Premier League.
The statement continued: "The board of directors of Hearts acknowledges it is not acceptable for Hearts to be in its current position in the league.
"The new manager's task will be to drive the club forward on the playing side to fulfil the club's ambitions.
"The move by the board of directors has the full backing of Hearts majority shareholder Vladimir Romanov."