The company said it would use the cash to build on existing business at 38 locations in 23 countries.
Entier already has a presence in Australia, Canada, Singapore, Trinidad and Tobago and the United States.
The Westhill firm specialises in onshore and offshore catering.
It serves meals to more than 4,500 people on oil and gas rigs and other remote installations around the world each day.
Entier also provides services such as cleaning, laundry and welfare.
Major clients in the offshore sector include Apache, Awilco Drilling, EnQuest, Rowan Drilling and Technip.
Onshore, Entier has developed the Fresh chain of cafes in Aberdeen, where it also offers catering and hospitality services.
Last year, the company acquired Scottish catering firm Wilde Thyme, which runs restaurants at Glamis Castle in Angus and the Glenturret Distillery in Perthshire.
Entier's revenues grew by 13% to £44.9m in the year to 30 September 2016, with pre-tax profits rising by 72% to £1.5m.
The Business Growth Fund was established in 2011 to provide growth capital for small and medium-sized businesses in the UK. It is backed by banking groups Barclays, HSBC, Lloyds, RBS and Standard Chartered.
Chief executive Peter Bruce said: "I've said in the past that I want to grow Entier into a £100m company and, with the backing of BGF, I believe we could do far better than that."
Aberdeenshire-based catering firm Entier is set to expand its overseas operations after securing a £6.5m investment from the Business Growth Fund (BGF).