A further 25 will be involved in a continuing training mission in Ukraine, the MoD said.
Defence secretary Michael Fallon said troops in the Baltic region would deter Russian aggression beyond Ukraine and reassure eastern European NATO members.
Fallon, who is in Brussels for a NATO meeting, also called on Russia to change its strategy in Syria where it has been carrying out air strikes.
He said British troops will be involved in training, evaluation and capacity-building missions in Poland and the three Baltic states.
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"If Russia wants to help here, the single most helpful thing they can do is use their influence on Assad to stop barrel-bombing his own civilians, their children, his own cities and villages. That's how Russia could help to resolve this conflict," he added.
Nineteen British teams in Ukraine have trained nearly 1,600 members of the Ukraine Armed Forces at eight training sites.
The operation is on course to have trained more than 2,000 Ukrainian troops by the end of the financial year.