The acquisition is Nitro's second since it launched in the UK in 2004.
It purchased the direct marketing agency River Communications in May last year and is now equipped to offer its clients digital marketing services, as well as advertising and direct.
Mook will continue to operate under its own name. However, the agency's 17 staff will move from their Shoreditch office into Nitro's premises in Covent Garden.
Mook's clients include the BBC, PlayStation, Reuters, News International, Channel 4 and Sport England. Its most recent win was the pan-European Diesel account.
The agency was founded in 1999 by its managing director, Tom Adams, the creative director, Tom Evans, and the director of operations, Roger Thelwell-Pichler.
Bruce Crouch, Nitro's executive creative director and managing director, said: "Digital was always high on our list of priorities. Since we identified Mook, its creative and new-business record has been excellent."
Adams said: "We have always held the view that truly integrated advertising depends on specialists sharing their skills under one roof. After five years of independence, this is a logical step that will help us pursue our ambitious expansion plans in the UK and give us access to other Nitro markets and clients."
He added: "These are exciting times for digital and Nitro is incredibly well placed to help us explore the channel's potential."
Nitro's clients include Nike, Coca-Cola and Credit Suisse. Earlier this month, news broke that its general manager, Enda McCarthy, had been hired by FCB London as its managing director (Campaign, 13 January).