Surrey-based HH described the deal as "one of the largest print management contract awards this year". It will include all of Asda's print, excluding point-of-sale and labels.
This is expected to grow in 2009 to include the Asda Magazine and Direct Big Book, which is currently printed by German-based printer Tiefdruck Schwann-Bagel.
The retail giant will also receive technical print buying services, vendor selection, production management, fulfilment, collation and mail-out support.
HH will provide Asda with an on-site print team at the supermarket's head offices, supported by resources at HH's own sites.
Chief executive of HH Print Management Robert MacMillan said: "Asda works with more than 150 suppliers currently.
"Despite an uncertain economic outlook, this is a clear message that UK retailers still value print in their overall marketing mix.
"Asda is set to increase its print spend so it was important that it installed the controls over brand accuracy, quality of production, time taken to market and cost control that this solution will bring."
HH said it was selected due to its cultural fit for Asda and experience in the retail and fast-moving consumer goods sectors.
Asda increases its print spend with multi-million pound contract
Asda is set to increase its print spend after awarding a multi-million pound contract to HH Print Management, following an extensive tendering process.