President Trump and his Polish counterpart will meet on Wednesday to make what administration officials said would be a major announcement on troop deployments, an outcome of talks over a Polish push for a permanent U.S. military presence at a proposed “Fort Trump.”

“It will be a significant announcement on the future of the security partnership,” a senior Trump administration official told reporters on Tuesday. The official described the move as a “new facet of our military-to-military relationship” that will strengthen...