The Bahrain base, named HMS Juffair, will be able to host the Queen Elizabeth class carriers and Type 45 destroyers as well as frigates and minehunters.
More than 70 ships and submarines, maritime patrol aircraft and 3,000 marines are taking part in the maritime portion of the exercise.
This latest rescue mission brings the total number of migrants rescued by Royal Navy ships in the Mediterranean to almost 7,000 since May.
The second of the UK's new supercarriers, HMS Prince of Wales, has passed a significant milestone after two halves of the ship were joined together.
Minister of State for Defence Procurement Philip Dunne has indicated defence investment greatly benefiting the Royal Navy over the next decade.
British frigate HMS Richmond has joined the EU mission in the Mediterranean to tackle migrant smugglers.
The Ministry of Defence have rejected claims that Britain risks not being able to crew its new supercarriers.
The destroyer will spend nine months in the Middle East after taking over from sister ship HMS Duncan.
A combined British and French naval fleet off Corsica used their helicopters and landing craft to evacuate civilians to safety.
It has been reported that as many as 23 Indian fishermen have been arrested after trespassing on Diego Garcia earlier in the month.