Joining them will be tens of thousands of troops from Nato and the Joint Expeditionary Force alliance, which includes Finland and Sweden.
The Ministry of Defence (MoD) said the action had been long planned, but that it had been enhanced in response since Russia invaded its neighbour in late February.
Commander Field Army Lieutenant General Ralph Wooddisse said: “The UK makes a significant contribution to the defence of Europe and the deterrence of Russian aggression.
“The British Army’s series of exercises is fundamental to both.
“The scale of the deployment, coupled with the professionalism, training and agility of the British Army, will deter aggression at a scale not seen in Europe this century.”
The UK deployment is expected to build to a peak of around 8,000 personnel operating in mainland Europe between April and June.
Defence Secretary Ben Wallace said: “The security of Europe has never been more important.
“These exercises will see our troops join forces with allies and partners across Nato and the Joint Expeditionary Force in a show of solidarity and strength in one of the largest shared deployments since the Cold War.”
Troops from the Queen’s Royal Hussars have been deployed for embedding in an armoured brigade in Finland, which shares an 830 mile land border with Russia.
Exercises alongside American troops are also taking place in Poland.