HSD currently has a turnover of £2m and a staff of 20.
Founder and MD Lesley Scott will continue to head up the agency, reporting to Gyro CEO Gary Brine.
Terms of the deal were undisclosed, but Scott said: 'It will mean we can engage with Gyro's global network and integrated platform to add more value to our clients' marketing campaigns.'
The acquisition follows Gyro's buyouts last year of healthcare marketing agency Woolley Pau, in November, and bio-chemical marketing specialist Cicero, in March.
HSD has clients in over-the-counter and prescription medicine, medical devices and complementary healthcare sectors.