The acquisition includes Blue's search subsidiary, Demand. It will give WPP access to a portfolio of digital expertise including online advertising, e-mail and search engine marketing.
Sir Martin Sorrell, the chief executive of WPP, said the move fell in line with "strategic goals".
Mark Read, the chief executive of WPP Digital, said: "Our clients continue to make a rapid transition to more digital and measurable approaches to their marketing. This means WPP Digital is now well positioned to serve our clients in this transition."