Drayton and finance director Niamh O'Donnell-Keenan left the company on Tuesday (11 October) afternoon, just two weeks after the new chief executive took the reins at the group.
The departures follow MacLennan's appointment last week of John Allwood, the former head of mobile telephone group Orange UK, as executive director of the newspaper group.
MacLennan was appointed at the end of August by the Barclay brothers, who bought the Telegraph Group in a 665m deal in June following a protracted auction.
Drayton was unavailable for comment, but it is unlikely that he will be surprised by the decision. Following MacLennan's appointment, he said that the new chief executive "will want to get a feel for the place, and in time he will want to put his own stamp on the team."
He has three months' gardening leave, but there is no agreement yet as to the financial arrangements.
A spokeswoman for the Telegraph confirmed that Drayton and O'Donnell-Keenan had stepped down on Tuesday afternoon but said that the group was making no further comment at this stage.
Story by Josh Brooks