The Prime Minister said the King "bears an awesome responsibility that he now carries for all of us", adding: "Even as he mourns, his sense of duty and service is clear."
Truss added the British people, the Commonwealth and all MPs must support Charles as he takes the country forward to a "new era of hope and progress, our new Caroleon age".
Her words were heard in a crowded but emotionally charged and silent chamber, the green benches populated by MPs dressed in black, as Parliament came together to mark the death of the nation's longest-reigning monarch.
Elizabeth, who died aged 96, was remembered during a minute's silence led by Commons Speaker Sir Lindsay Hoyle.
The Commons and Lords will sit on Friday and Saturday to allow tributes to the Queen. Proceedings will pause at approximately 6pm while Charles makes his address to the nation.
Truss told the Commons: "On the death of her father King George VI, Winston Churchill said the news had stilled the clatter and traffic of 20th century life in many lands.
"Now 70 years later in the tumult of the 21st century life has paused again. Her late Majesty Queen Elizabeth II was one of the greatest leaders the world has ever known."
Truss said the Queen "remained determined to carry out her duties" even at the age of 96, noting: "It was just three days ago at Balmoral that she invited me to form a Government and become her 15th prime minister.
"Again she generously shared with me her deep experience of government, even in those last days."
Truss said the Queen's devotion "remains an example to us all" and hailed her for having "reinvented the monarchy for the modern age".
"Her late Majesty's image is an icon for what Britain stands for as a nation, on our coins, on our stamps, and in portraits around the world.
"She was loved and admired by people across the United Kingdom and across the world.
"One of the reasons for that affection was her sheer humanity.
"She reinvented monarchy for the modern age. She was a champion of freedom and democracy around the world ... She was willing to have fun."
Truss added: "During her first televised Christmas message in 1957 she said: 'Today we need a special kind of courage so we can show the world that we are not afraid of the future'. We need that courage now.
"Today we show the world that we do not fear what lies ahead."
On the King, she said: "His Majesty King Charles III bears an awesome responsibility that he now carries for all of us.
"He has already made a profound contribution through his work on conservation, education and his tireless diplomacy.
"We owe him our loyalty and devotion."
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