The pair will join the agency as senior art director and senior copywriter, respectively.
Mannion has been at DraftFCB as an art director for five years, while Singh joined the agency 18 months ago, when the pair first teamed up.
During their time at DraftFCB, Mannion and Singh worked on clients including Stella Artois, Heineken, Twinings and General Motors.
At Modem, the pair will devote most of their time to the agency's GM business because of their experience of working on Saab and Vauxhall at their previous agency.
They will also work on Modem's Hewlett-Packard business, which it recently picked up from McCann Erickson after a competitive pitch.
The business is a European account and covers HP's Technology Solutions Group and the Personal Systems Group.
Mannion said: "I'm really excited about the move and especially looking forward to working with Chris Clarke (the executive creative director) - we'll be able to learn so much from him. The agency has a great client list and is winning a lot of business."