Charles spoke to a joint session of the House of Representatives and the Senate after earlier meeting with President Donald Trump in the Oval Office.
Mr Trump had used similarly warm words in welcoming the King and Queen to the White House despite recent tensions between the long-time allies.
During his remarks, the president praised the enduring relation between the nations and also mentioned the late Queen Elizabeth II, drawing attention to a tree she had planted as a sapling.
The build-up to the visit had been marred by tensions between the nations over the US military action against Iran and the subsequent blockade of the Strait of Hormuz.
In return, Mr Trump had criticised a lack of support from the UK for his actions.
While the King and president chatted in the Oval Office the Queen and first lady met students.
