Etrinsic is to provide a range of print management and marketing services to both clients, which will include print buying and logistics, direct mail, design and data management.
Belfast and Birmingham-based Laser UK offers credit and customer programmes, while Baxi Group, which has offices in Warwick, Erdington and Derby, is a manufacturer and supplier of heating systems.
Matt Bird, managing director of Etrinsic, said the company is enjoying a time of significant growth "at a time when many of our competitors are moving in the opposite direction".
He added: "Clients are looking at what they spend and the value they are getting. It's about knowing where print fits in with other media, but rumours of its demise are more than a little exaggerated."
Jayne Licari, Laser UK marketing manager for strategic projects, said: "We went through the tender process specifically to drive savings and add value to what we do. We were impressed by the staff and the level of experience at Etrinsic.
"The quality of their people really stood out and we knew we could work well together."
Last month, the Solihull-based Etrinsic signed the fourth renewal of its contract with insurance, investment and pensions group LV=.