Snowball was founded in 2003 and provides customer management and data insight services to clients including Bang & Olufsen, Dunhill, Hulsta, Meridian and Trailfinders.
Management of the agency will remain unchanged, with Damian Bentley continuing as Snowball's managing director.
In 2008, Snowball generated revenues of £2.27m and pre-tax profits of £878k.
Nicholas Green, Tangent's joint chief executive, said the enlarged business will offer clients services that link data, strategy and creative to execution, "all underpinned by our proprietary technology platform".
Tangent, which is listed on technology stock market AIM, said the acquisition "transforms [our] skills and capabilities in the area of data insight and analytics".
The initial consideration of £1.03m in cash is being funded from Tangent's existing resources. The maximum further consideration of £2.18m in cash and shares is subject to Snowball meeting three-year targets over three years.
Green said Tangent retains £750k of net cash following payment of the initial consideration and will consider further acquisitions.