WARSAW—The U.S. will station 1,000 troops and put the headquarters for an armored brigade in Poland, President Barack Obama announced Friday, laying down a strategic military marker in Eastern Europe aimed at deterring Russian aggression in the region.

The moves exacerbate tensions with Russia, which has repeatedly denounced military buildup in the region. The U.S. commitment sends a signal of support to Europe at a time of heightened security concerns and uncertainty about its cohesion since the U.K. voted to exit the European...