Kainos will invest Â£900,000 as part of a fundraising round of Â£3.5m, led by existing shareholder Kernel Capital.
Cirdan Imaging, which is also based in Belfast, has a customer base in the US, Canada, Australia and the Middle East.
Kainos envisages that Cirdan Imaging could become an important reseller of its Evolve healthcare software in those territories.
As part of the dealt, Cirdan Imaging has entered into a five-year licensing agreement for Evolve software.
Brendan Mooney, the chief executive of Kainos, said the new relationship will "open doors for both businesses, creating interesting new growth opportunities".
Cirdan Imaging was founded by Dr Hugh Cormican in 2010.
Dr Cormican was also a founder of the Andor Technology firm that makes high-performance digital cameras for use in scientific research.
He said the investment in Cirdan Imaging would be used to strengthen its laboratory information software product and grow its customer base.
Belfast-based software firm Kainos has bought a 10% stake in Cirdan Imaging, a medical diagnostics company.