The deals are worth £24m between them.
Cheeze, previously owned by founders Katherine Jerman and Jamie Riddell, is primarily a digital direct marketing agency and has offices in Ipswich, London and Leeds.
Its core services are planning and buying for digital media campaigns, but it also offers search engine marketing, customer relationship marketing and digital direct marketing consulting.
Unaudited financial reports for last year show the company had turnover of £10.5m, a profit before tax of £768,000 and net assets of £950,000.
DMG chief executive Ben Langdon said: “We have defined our space as the digital direct model.” He added that Cheeze “naturally complements” its other digital businesses, such as digital interactive agency Inbox and direct marketing specialists Dig for Fire.
Digital Marketing Group expands with acquisitions
Digital Marketing Group, the owner of marketing firms Dig for Fire and HSM, has acquired digital agency Cheeze and data analysis company Jaywing.