US Secretary of State Condoleezza Rice - who signed the deal in Warsaw - said Moscow's earlier warning that the base on Polish soil could become a target for a nuclear attack bordered on the bizarre.
Last month, the US signed an agreement with the Czech Republic to base tracking radars there as part of the defence system.
Washington wants the sites to be in operation by about 2012.
'Imaginary' threat
The Russian foreign ministry said the planned missile shield was aimed at weakening Moscow, describing it as part of "US efforts to change the strategic balance of power in its favour".
INTERCEPTOR MISSILES
Look like ordinary missiles, but warheads are not loaded
Intended to destroy target with kinetic energy
Closing speed at interception is 24,000km/h (15,000mph)
It said the shield was "one of the instruments in an extremely dangerous bundle of US military projects involving the one-sided development of a global anti-missile system".
The statement also dismissed US claims of a missile threat from Iran as "imaginary".
However, the ministry said that Russia was still prepared to continue dialogue on the US missile shield with all parties involved.
'Aimed at no-one'
In Warsaw, Polish Prime Minister Donald Tusk said the negotiations had been "tough, but friendly", adding that the deal would make both Poland and the US more secure.
Ms Rice said the signing of the document was an extraordinary occasion.
She said the agreement would help Nato, Poland and the US respond to "the threats of the 21st Century".
Ms Rice also emphasised that the missile system was "defensive and aimed at no-one".
One-Minute World News
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