They join Saatchis from JWT where they were creative directors working on accounts including Smirnoff, HSBC, KitKat, MTV and Radio Advertising Bureau.
Quinn and Norcutt, who have also worked at Leo Burnett and Abbott Mead Vickers BBDO, will also work across other clients.
Their creative highlights include BT's "bringing people together", Smirnoff's "triple distilled type" and KitKat's "pause". They have also won three Cannes Lions, a D&AD silver Pencil and four BTAA Arrows.
The pair started out at Leo Burnett, working on McDonald's, Heinz and Kellogg, before joining AMV BBDO in 2001, where they worked on accounts including BT, The Economist and BBC Radio 5 Live. They joined JWT in 2004.
Paul Silburn, the Saatchis creative partner, said: "I've known Laurence and Mark for over ten years and in that time I've watched them consistently produce excellent work. Yet I believe their very best work is still to come and that it will happen at Saatchi in a very interesting way."