Crisp, who has worked at Lowe for the past 18 years, will take the top TV job at The Red Brick Road when he joins the agency on Monday.
Red Brick Road is currently working on its inaugural advertising for Tesco. It took over the account on 6 March. Crisp said his strong relationship with the supermarket client during his tenure at Lowe was one of the reasons he decided to make the move.
He added: "Moving to Red Brick Road is a very fine opportunity to work for a group of very talented people. Opportunities like this don't come around that often."
At Lowe, Crisp most recently worked on TV ads including "ice-skating priests" for Stella Artois and "Stunt City" for Sure. He cited 1998's Cannes Grand Prix-winning "litany" ad for The Independent as his personal highlight at Lowe.
Crisp joined the then Lowe Howard-Spink in 1988 from Ogilvy & Mather.
He was promoted to the post of head of TV in 1989. He will be replaced by Lowe's deputy head of TV, Jane Rattle.