The deal was signed by Andrzej Kremer, the deputy Polish foreign minister, and John Rood, the US chief negotiator at a brief ceremony in Warsaw, Reuters reported.
However it must still be approved by Poland's parliament.
The agreement follows 18 months of negotiations and comes at a time of tension between the US and Russia over the conflict in Georgia.
'Security threat'
Tusk also said the deal includes a "mutual commitment" between the two nations to come to each other's assistance "in case of trouble".
"We have finally got understanding of our point of view that Poland, being a crucial parner in Nato and an important friend and ally of the United States, must also be safe," he said.
But after the news emerged Sergei Lavrov, the Russian foreign minister, cancelled a visit to Warsaw that had been scheduled for September, Radoslaw Sikorski, his Polish counterpart, told reporters on Thursday.
The US says the shield is to prevent potential missile attacks by "rogue states", including, it says, Iran, and is not directed against Russia.
But Moscow considers the shield a security threat designed to undermine Russia's nuclear deterrent.
It has vowed to retaliate if Poland, and also the Czech Republic, go ahead with any deals on the shield.
The Czech Republic signed a deal with the US in July this year to place radar units, part of the missile shield system, inside its borders.