The pitch is believed to have started with five agencies and ended in a three-way shoot-out between Cubitt, GCI Group and Financial Dynamics.
Brocklebank-Fowler declined to comment on the account win but it is understood the agency stands to pick up more than £400,000 in fees for the year-long deal.
The brief covers five major European markets - including the UK, France and Germany. Outside London, the agency will work with affiliate agencies.
It is thought the work will focus on building the Ashurst brand among corporate audiences, including major banks and industrial concerns.
The 175-year-old law firm has 700 lawyers and 11 wholly-owned offices across Europe. The company consistently ranks in the top three of advisers with the highest number of clients in the FTSE 100.
The Cubitt team will report to a panel of partners led by senior partner Geoffrey Green and to recently-appointed global brand director Marina Galanti.