They will conduct manoeuvres in the wide spaces of a former member of the Warsaw Pact which Nato spent 35 years preparing to fight.
The British Army is delighted with the new training facilities among the rolling woodland and lakes of Prussia, which dwarf anything available in Britain or Germany, where it is increasingly cramped. But the deal has a greater importance.
The arrangement bridges the gap between Poland - a leading candidate for Nato membership - and Ukraine, which has until recently opposed expansion of Nato and is unlikely to join. It also gives Britain a foothold in eastern Europe.
Poland and Ukraine have a joint population of more than 80 million - the same as Germany - and, at 450,000-strong, Ukraine's armed forces are Europe's largest after Russia's and Turkey's.
Ukraine's Defence Minister, Lieutenant General Oleksandr Kuzmuk, signalled that Ukraine's opposition to Nato's eastward expansion had softened. "It is the sovereign right of any country to decide to which bloc they want to belong to. For us, it is the will of our president, parliament and the Ukrainian nation that we are a non-bloc nation," he said. "But we are for cooperation with any of our neighbours, east, north or west." The Polish Defence Minister, Stanislaw Dobrzanski, stressed that Poland's desire to be in Nato was not aimed "to be against anyone or threaten anyone".
Ukraine has also been concerned that the extension of the Nato nuclear guarantee to Poland might mean nuclear weapons being based on Polish soil, although with modern nuclear weapons that would not be necessary. "Ukraine was the third nuclear state in size [after the US and Russia] but it has relinquished its nuclear status," Lt Gen Kuzmuk, a former Soviet tank brigade commander, said. "So you must take account of Ukraine's view that nuclear weapons should remain where they are now."
Even more extraordinary than the reconciliation between former Nato and Warsaw Pact enemies is the warming of relations between Poland and Ukraine, after centuries of territorial disputes and bloodshed.
The Ukrainian and Polish ministers were joined by the British armed forces minister, Nicholas Soames. They confirmed they had agreed a trilateral defence arrangement which would include the use of each other's training facilities and a joint parachute exercise. A joint Polish-Ukrainian battalion is to be set up to specialise in peacekeeping operations.
The most radical innovation may be the British use of air-to-ground ranges in Ukraine.
The British were delighted with the 400-square-kilometre training area. After nine days of training by the individual armoured battle groups (about 1,000 troops each), they combine for a four-day rehearsal of full armoured warfare.