Barack Obama, the US president, decided last year to scrap a plan by George Bush, his predecessor, to deploy a longer-range missile-defence system in Poland and the Czech Republic, opting instead to use smaller sea and land-based missile interceptors.
While there were reports last year that Poland was unhappy with Obama's decision to abandon the Bush plan, Sikorski said Poland preferred the new approach.
"When President Obama announced the new configuration of the system, we did say that we liked the new configuration better but I think you didn't believe us," he said.
"I hope now that we have signed the annex, I hope you do believe us."
Clinton sought to counter Russian objections to the plan, which it views as a danger to its own nuclear deterrent.
"This is not directed at Russia. It is a defensive system to protect our friends and allies and our deployed forces," she said.
"The real threats come from the development of short and medium-term missiles on a faster timetable from Iran."
Clinton refused to specify a date as to when the new defence project may be deployed on Polish soil, but defence experts have said it is likely to be ready in 2018.
The two countries also announced plans to co-operate on the exploitation of shale gas.
Clinton began her day by laying a wreath at a memorial to pay tribute to the victims of the April 10 air crash in Russia that killed 96 people, including Poland's president and its military commanders and central bank governor.
She was to end her visit to Krakow by giving a speech at the Community of Democracies, a 10-year-old inter-governmental group that aims to promote democracy and civil liberties.