The move marks the most aggressive show of U.S. force since Russia's presence in Ukraine began. American troops will be placed in Poland, Lithuania, Latvia and Estonia.
"I think if there's a message to Moscow, it is that we take our obligations very, very seriously on the continent of Europe," said Admiral John Kirby, Pentagon spokesman.
The deployments were announced just hours after Vice President Joe Biden, who was in Ukraine, issued a stern warning to Putin.
"We have been clear that more provocative behavior by Russia will lead to more costs and to greater isolation," Biden said.
Biden said time is running out for Russia to move its tens of thousands of forces from Ukraine's eastern border and its supporters out of government buildings.
The United States also wants to know the fate of an American journalist Simon Ostovksy with VICE news. Ostovsky was reporting from Ukraine before he was arrested by unidentified people in uniform in Eastern Ukraine.
American troops moving in for exercises will be in Europe until the end of the year.
