The ship carries the joint staff who will command the deployment - drawn from the Plymouth-based headquarters of 3 Commando Brigade Royal Marines and the staff of the Commander of the Amphibious Task Group.
It marks the first deployment of the military force which comprises nine nations including the UK, Denmark, Estonia, Finland, Latvia, Lithuania, the Netherlands, Norway and Sweden.
At its peak, a total of 3,850 sailors, marines, soldiers, and airmen will take part, along with more than 17 naval vessels in the Baltic region.
Captain Peter Laughton, the Commanding Officer of HMS Albion, said:
"This represents the largest UK-led operational deployment of a military force in Europe for decades and demonstrates our ability to react quickly and decisively to any crisis in the world."