The project has been a major source of tension with Russia and had looked stalled since the Polish government of Donald Tusk sought new demands after taking office in November.
Sikorski did not outline the terms of the deal, but in a joint appearance with Condoleezza Rice, the US secretary of state, the two officials suggested that the US would help with Polish air defenses, which Poland has asked for in the deal.
Rice said: "We understand that there is a desire for defense modernisation in Poland, and particularly for air defense modernization in Poland.
"This is something that we support because it will make our ally, Poland, more capable, it will make Poland, as the foreign minister has said, more able to operate with us."
Sikorski said that negotiators would continue to work on the details of an agreement that would allow the US to install 10 interceptors as part of a long range European missile defense system.
He said: "We are not at the end of the road as regards negotiations. We are in the middle of the road. We have an agreement in principle."
Russia has threatened to retarget nuclear missiles at Poland to counter what it sees as a US attempt to undermine the Russian military deterrent.
Seeking to reassure Moscow, Sikorski said: "The reinforced Polish air defenses are not directed against anybody. They are to enable Poland to be a stronger Nato ally with the United States, to enable Poland to take part in operations, in out-of-area operations, in joint operations."
But the air defense system that Poland has asked for help in building would seem to be aimed at addressing concerns about Russia's threats.
If the two sides reach a final deal, it would seem to vindicate Tusk and Sikorski's strategy of asking more from Washington in exchange for Poland's support in military operations in Iraq and Afghanistan, as well as the missile defense system.
The previous Polish government of Jaroslaw Kaczynski, the former prime minister, who opened talks with the US early last year, firmly supported the plan without the additional demands.