The agency pitched against Lowe and McCann Erickson, two of GM's roster agencies.
DLKW will create a multimedia campaign pushing the technological elements of the car and aiming to give it a more upmarket appeal.
The work will run in Europe across TV, press, outdoor and online ahead of the launch later this year.
Insignia, previously called Vectra, will be unveiled at the London Motor Show in July and launch in November.
James Pool, the DLKW joint managing director, said: "GM's designers and engineers have delivered a truly great flagship product. It's a privilege for DLKW to win the responsibility for the launch of the Insignia brand."
DLKW's last major pan-European launch for GM was the Vauxhall Corsa in 2006. Featuring the "c'mon" animated glove puppets, the campaign was used to position the car as a fun and stylish option for twentysomethings.