Grout will be responsible for the day-to-day running of the UK office, with an emphasis on attracting new business.
His appointment will free up Chris Gordon, the agency's international chief executive, to focus on developing a network for the agency beyond the US and UK.
Grout has more than 15 years' experience in direct marketing. He has had two spells at Rapp, eventually becoming the agency's managing director for UK and Europe, a role he left in 2007. While at Rapp, he worked closely with Gordon, who was its European chief executive.
He has also been the managing director of Carlson Marketing, and had a spell running the Ford UK and Jaguar Worldwide accounts at Wunderman.
Targetbase Claydon Heeley was the result of a merger between the UK direct marketing shop Claydon Heeley and US-based data agency Targetbase in July 2008. Since its inception, the agency has picked up business for brands including Selftrade and Jobsite.
Grout said: "Its fantastic to have the opportunity to help build on what has been a successful start to the new agency's life."