A 500-strong battalion will be deployed to Estonia and 150 troops will be based in Poland to "reassure" these countries, the defence secretary said.
It is part of a Nato commitment made after Russia's annexation of Crimea from Ukraine in 2014 to have four new battalions on its eastern flank.
Michael Fallon said it aims to "deter Russia from any further aggression".
Eastern Nato countries "feel enormous pressure from Russia doing large exercises on the border, flying over their airspace and so on," he said.
The UK is also to take over the leadership of a standby force in 2017.
Mr. Cameron, who is due to announce the deployment at a Nato summit in Warsaw later, said: "This summit is a chance for us to reiterate our strong support for Ukraine and our other eastern allies to deter Russian aggression.
"Actions speak louder than words and the UK is proud to be taking the lead role, deploying troops across Eastern Europe.
"It is yet another example of the UK leading in Nato."
Nato Secretary General Jens Stoltenberg says Russia's use of force against Ukraine "has really changed our security environment. Nato has to respond".
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