Lambert's promotion will leave Mike Dodds in charge of the customer relationship marketing agency.
Reporting directly to Gary Leih, the chairman and chief executive of the Ogilvy Group UK, Lambert will be responsible for the day-to-day running of the creative agency, with a particular focus on client relations.
Taking up his post on 1 September, Lambert will fill the gap left by the former O&M chief executive Paul Jackson, who vacated the position in February to take the new role of managing director of client services on the international American Express business.
The appointments follow this year's restructure of the company, which saw the 11 separate Ogilvy businesses brought together under the Ogilvy Group UK banner.
Lambert said: "It has been an exciting ride working with Mike and I am certain it will be equally exciting building on the recent successes of O&M London.
"I'm looking forward to finding new and better ways of collaborating with the rest of the Ogilvy Group, and making our shared '360-degree branding' approach a reality for our clients."
Lambert began his career at O&M Direct in 1988, before moving to the network's Hong Kong operation in the early 90s to work on AmEx.
After returning to the UK and working on clients such as Bupa, GlaxoSmithKline and Huggies, he spent a short time at Euro RSCG.
Lambert returned to WPP via Red Cell, where he worked on the Alfa Romeo and Bank of Scotland accounts, before rejoining O&M in 1997 to run the AmEx business.
- Comment, page 48.