The Polish locations for the US military named in the declaration include the south-western city of Wroclaw, the central town of Lask and the southern town of Lubliniec.
The location for an US armoured brigade battle group is still being discussed.
The latest document adds details to a previous declaration signed by Duda and Trump in June, which confirmed the presence of 4,500 US military personnel in Poland and announced the deployment of about 1,000 more.
Poland's north-western town of Drawsko Pomorskie was designated as the main location for a battle training centre to be used by Polish and US armed forces. Strachowice, a western district of Wroclaw, will be the location of a loading/unloading air base. A squadron of US unmanned aerial vehicles will be located in Lask.
The central village of Powidz will be the location for an air battle brigade of a combat logistics battalion. Lubliniec is to become home of a special forces facility, while Poznan will be the headquarters of the forward division command and a support group for the US Army.
In the declaration, Poland and the US stated they will continue to strengthen their strategic and defence relations to improve security of both countries as well as NATO.
Poland will cover part of the costs of the presence of US soldiers on its territory, Trump said at the meeting.
Poland is also to build necessary infrastructure, Trump added after signing, together with President Duda, a declaration on the increased presence of US troops.
The US president noted that both countries are cooperating in numerous areas, but mainly in the military field and stressed that the US will move more troops to Poland.
US Secretary of State Mike Pompeo added that the declaration is proof of mutual respect and friendship. He added that most likely the US will move some of its units to Poland from other regions of Europe rather than from the US.
Trump also announced that he will visit Poland soon, adding he had fond memories of his last visit to the country.
Trump was originally scheduled to visit Poland at the beginning of September, among others to attend observations of the 80th anniversary of the outbreak of World War II, but was forced to change his plans owing to hurricane threats in Florida.
Asked about prospects for visa-free travel to the US for Polish citizens, Trump said this could happen very soon. He added that according to reports from US Ambassador in Warsaw Georgette Mosbacher, Poland has now met the visa waiver criteria.
Visa-free travel to the US can be granted only if the visa refusal ratio for a given country is below 3 percent. Until now, Poland's refusal ratio was above this threshold.
The US president also said he and his Polish counterpart had discussed aid to Ukraine. Trump complained that the United States was shouldering most of the cost of aiding Poland's eastern neighbour whereas Western European countries failed to make meaningful contributions, naming Germany and France in this context.
Ukraine has been torn by conflict with pro-Russian separatists in the country's eastern regions and has suffered the loss of the Crimean Peninsula, which Russia annexed in 2014. (PAP)
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