The award, which follows wins last month with Midlands-based Laser UK and BAXI Group, covers procurement of a range of print including residents' newsletters and communications, stationery and mailings.
Etrinsic managing director Matt Bird said: "This is yet another new business win for Etrinsic in just a few months and further proof that companies and organisations are turning to us to help not only get the most from their current print spend but also to develop a strategic plan to deliver outstanding value for the future."
Midland Heart, which manages 32,000 homes and provides care and support services in over 6,000 settings, said that delivering the best possible return on its print spend was a requirement of the contract award.
Sarah Clee, head of marketing and communications at £140m-turnover housing association, added: "We were looking for a company who could see ahead and alter their working practices to get even better value for money for us.
"We awarded the contract to etrinsic because we felt that they were best able to provide for our existing needs and, more importantly, to support the processes we wanted to adopt in the future."
Etrinsic provides a range of print management and marketing services including print buying and logistics, direct mail, creative design and data management.