The account was moved out of the incumbent, Mother, without a pitch.
W&K was added to the Guardian Media Group's roster in August last year after it picked up the £5 million flagship Guardian business.
It won the account in a two-way shoot-out against The Red Brick Road, following a pitch process that lasted more than six months.
Mother picked up The Observer business in December 2001 after a five-way pitch.
Marc Sands, the Guardian Media Group marketing director, said of the W&K appointment: "We're increasingly running promotions across both papers and it makes little sense to have two agencies working separately on projects that are frequently joined.
"The pitch W&K did last year was fantastic and its understanding of a difficult brand has been exemplary."