He will be responsible for all worldwide operations, with a focus on European expansion. Agency.com employs 400 staff in London, San Francisco, Dallas, Chicago, New York and Amsterdam.
Eastman will relocate to New York in the summer, as soon as he has named a London successor. An internal appointment is widely expected.
In his new role, Eastman will report to Jeremy Pagden, the president and chief executive of Tequila\Worldwide.
Eastman said: "I want to roll out our creative, planning and media model across the network. We will look to expand to four or five offices in Europe before we start looking at Asia next year."
Agency.com has also appointed Dave Johnson, the managing partner of Agency.com's Chicago office, to the new role of president of Agency.com North America.