The three-year contract award, which is worth around £2m annually, is the first to have been announced by the former St Ives Bradford business since it rebranded last month.
Andy McGrath, national marketing manager at Hillarys, said: "Overall, GMP's package of suitable presses for our products, good customer service track record, together with competitive pricing won the day. We look forward to working with them in the New Year."
The so-called "Door to Door" print contract includes the printing of insertions for national and local media channels.
The £35m-turnover former St Ives Direct business in Bradford was sold to Cogent B2B in an £8m deal in September and has since reported positive trading in its first quarter.