RJW will retain its brand but will collaborate with The Mission's other healthcare-focused business – full-service agency Solaris Health.
The acquisition consists of an initial consideration of just under £2m, £1.88m in cash and £100,000 through shares, and a further consideration of up to £4.25m payable subject to financial performance between now and 2020, of which 95 per cent will be paid in cash.
Established in 2008, RJW had a turnover of £1.6m and profit of £400,000 in the year to 31 March 2016. Clients include AstraZeneca, Shire and Novartis.
It has 30 staff across the UK, the Netherlands and Sydney offices, as well as associates across North America and elsewhere in continental Europe.
RJW co-founder and director Neil Johnson said he hoped the business had "found the perfect partner with which to grow".
Other agencies in The Mission group include Speed Communications, Mongoose Marketing and Bray Leino. Total group revenue in 2016 increased by nearly 10 per cent £65.9m, with profit before tax rising at a similar rate to £7m. Chair David Morgan said at the time of the results announcement that the group continued "to seek out attractive acquisition opportunities".