The incumbent on both the creative and media businesses, the Kent-based full-service agency Nexus/h, has lost a client it had serviced for more than two decades.
VCCP also pitched for the creative account in a process that was handled through the consultant Brian Jacobs & Associates.
The Japanese car and motorcycle manufacturer has yet to appoint an agency to handle its media planning and buying, but has whittled down the competing agencies to Arena Media and the7stars. UM London had also pitched for the media account.
The Red Brick Road will be responsible for handling Suzuki's national and local through-the-line advertising.
Suzuki declined to comment on the appointment but James Osborn, the client services director at Nexus/h, said: "Having worked and grown up with Suzuki over 20 years, we are extremely proud in terms of what we have achieved both in media, creative and overall business results.
"We wish Suzuki and The Red Brick Road every success for the future."
Last year, Suzuki launched a major ad campaign, "designed for life", for its new Swift car marque.