The ships will now head to Falmouth, Cornwall, before leaving the UK later this week.
They will be deployed from the east of Africa to the west coast of the USA during the next five years.
Acting as the eyes and ears of the Royal Navy, both ships will work with Britain's allies to carry out security patrols to deal with drug-running, smuggling, terrorism and other illegal activities.
They will also take part in exercises with other navies and Armed Forces, with their patrol area stretching across both the Indian and Pacific oceans - extending as far north as the Bering Sea and as far south as Tasmania and New Zealand.
No permanent home has been assigned to the pair - instead they will use Pacific bases and ports which best meet their needs and mission.
Watch: HMS Tamar - a guided tour around the Royal Navy's 'greenest' ship.
Lieutenant Commander Ben Evans, HMS Spey's Commanding Officer, said "two-thirds of the world is our playground".
"We are going to places that the Royal Navy has not visited in a long time – that's really exciting."
Each ship is crewed by 46 sailors, with half of the crew trading places with shipmates from the UK every few weeks.
The constant rotation allows the Navy to get the most out of the ships: the crews are at sea for up to nine months of the year, while the vessels are ready for operations all-year-round.
Watch: CSG21 - Timelapse of HMS Queen Elizabeth arriving in Japan as the aircraft continues her deployment in the Indo-Pacific.
The crews will be joined by extra personnel – up to 52 Royal Marines or troops in a dedicated mess – or mission-specific equipment to deliver humanitarian aid or help with evacuations.
Leading Weapons Engineer Alex Twidell, serving on HMS Tamar, said the deployment will be an "amazing experience".
"The opportunity to go to the Indo-Asia Pacific offers an exciting opportunity that very few in the newest generation of Royal Navy sailors have had the chance to partake in."
HMS Spey and HMS Tamar will arrive in the Pacific following the maiden deployment of HMS Queen Elizabeth and the Carrier Strike Group in the region.
Cover image: HMS Tamar leaves Portsmouth (Picture: Royal Navy).