Brittin will retain his role as head of UK client sales in addition to taking the role of director of UK operations. Mark Howe remains in charge of agency sales.
Brittin joined Google in January 2007 from Trinity Mirror where he was director of strategy and digital.
He said: "We are working with hard with our UK partners and customers to help them take advantage of the online opportunity, particularly at this time."
Woodside has been at Google for five years and before heading up our UK, Ireland and Benelux operations he opened up our operations in Eastern Europe.
Omid Kordestani, Google's senior vice-president of global sales and business development, said: "In the five and a half years that Dennis has been at Google (that's over half our company's lifetime) he's brought incredible integrity and entrepreneurialism to everything he's done.
"I remember Dennis setting off from Mountain View in 2005, a year and a half after he joined, to start our direct sales operations in Eastern Europe, which he quickly transformed into a substantial part of our business."
"He also set up our inside sales operations in Dublin - again building it from scratch. In September 2006, he became our vice president for the UK, Ireland and Benelux where he's helped to create a first class team as well as establish very positive relationships with our big partners on both the advertiser and agency side."