The deployments are above and beyond the 8500 troops the Pentagon put on alert last month to be ready to deploy to Europe if needed.
Together, the moves aim to reassure jittery NATO allies in the face of a Russian military build-up near Ukraine while avoiding new deployments to Ukraine itself, which is not part of NATO.
A source familiar with the details said 1700 would deploy from Fort Bragg in North Carolina to Poland and another 300 from the base to Germany.
About 1000 Germany-based troops would to head to Romania, the source said.
The Pentagon said it was not ruling out additional deployments beyond those announced on Wednesday.
"It's important that we send a strong signal to Mr Putin and, frankly, to the world that NATO matters to the United States and it matters to our allies," Pentagon spokesman John Kirby said at a news briefing, referring to Russian President Vladimir Putin.
Washington's decision to boost troop levels in Eastern Europe is a "destructive step," says
Russian Deputy Foreign Minister Alexander Grushko said the decision to boost US troop levels in Europe was a "destructive step" that will heighten tensions.
He said the move will narrow the room for political decisions revolving around tensions in Ukraine, "to the joy of the authorities in Kyiv".
Earlier on Wednesday, the Spanish newspaper El País published what it said was the answers of NATO and the United States to Russia's proposals for new security agreements, which had so far been kept under wraps.
According to the documents posted on the internet, the US and the military alliance make it clear that a large part of the Russian proposals are not acceptable to them.
At the same time, NATO and the US show themselves open to concrete negotiations and new agreements.
According to its response to Russia, the US is prepared to rule out the permanent stationing of combat troops and ground-based missile systems in Ukraine if Russia also makes corresponding commitments.
In its written reply, the US offered transparency over its Romanian and Polish missile sites if officials in Moscow did the same at two sites in Russia.
NATO and the US have called for an end to the current Russian troop deployment on Ukraine's borders as a prerequisite for successful negotiations.
This is central to substantial progress, according to the NATO response.
The authenticity of the documents was confirmed to the DPA news agency by NATO sources.
In view of the Russian deployment of more than 100,000 soldiers near Ukraine, there are fears that the Kremlin is planning an invasion of the former Soviet republic.
However, it is also considered possible that fears are only being stirred up in order to persuade NATO members to make concessions in response to demands for new security guarantees.
Russia wants to persuade NATO to rule out further enlargement to the east, and in particular the inclusion of Ukraine.
It is also demanding a withdrawal of NATO troops from eastern European NATO members.
with Reuters
