The acquisition reinforces Tangent's long-term growth strategy as it aims to become one of the country's top ten digital marketing businesses.
Lateral, which moves into Tangent's offices today (March 6), will take with it a client list that includes RSPCA, Hachette UK, Which? and Paco Rabanne.
Jon Bains, co-founder and planning director of Lateral, said the decision to join Tangent "felt like the perfect move".
Bains said: "We've been looking to move to the next step with Lateral for some time.
"Our ambition has always been to build a world-class digital marketing business with a true delivery focus and now, with Tangent, there is an amazing opportunity to make a significant impact on the market together, even in these trying times."
Nicholas Green, chief executive of Tangent Communications, said the acquisition was part of Tangent's ongoing investment plan.
Green said: "[It] helps us to create a business that is totally relevant for industry needs, both today and tomorrow."
Tangent Communications companies include digital agency Tangent One, direct marketing agency Tangent Direct, marketing technology group Tangent Labs and digital print companies TOD and Ravensworth.