Phillips, the doctor and pharmaceutical exec who set up Double Helix in 1995, will remain in charge when Interpublic Group takes over the firm.
Although the companies did not disclose financial terms, sources familiar with the situation said McCann Health, a division of Interpublic, would pay £35m upfront, with up to a further £15m dependent on future revenue.
Cavendish Corporate Finance advised Double Helix during the sale.
Double Helix has more than 90 staff and offices in London, Singapore and the United States.
Cavendish healthcare partner Gordon Hamilton said the two firms were a good fit due to Double Helix’s exposure to fast-growing markets such as Asia Pacific.