The 75-year-old Monarch conveyed her "deep gratitude" on Monday evening in a taped speech broadcast on the eve of her abdication.
Beatrix said she had "shared both joy and national pride" with her people as well as their "sorrow and anxiety."
She said Crown Prince Willem-Alexander was "well prepared" to become monarch and would "act without regard to personal preference."
"Now that my oldest son is to take over this fine and responsible job tomorrow, it is my deep wish that the new royal couple will feel themselves supported by your loving trust," the Queen said.
"I am convinced that Willem-Alexander will apply himself with true devotion to everything a good king is obliged to do," she added.
The nationally televised address aired as the Queen hosted a dinner at the newly renovated national museum, the Rijksmuseum. In attendance were the Queen, Willem-Alexander, his Argentinean-born wife, Maxima and nobility from 18 nations, including Britain's Prince Charles and Japanese Crown Prince Naruhito.
Willem-Alexander, 46, is to officially take the helm on Tuesday when the Queen signs the Abdication Act formalizing the once-in-a-generation change of royal titles. He will then take an oath to observe the Dutch constitution at Amsterdam's Nieuwe Kerk.
Supporters of the royal family began assembling outside the Royal palace on Monday, with more than a million people expected in Amsterdam to witness the ceremony. As part of security arrangements, the city's aerospace was closed for three days Monday and an estimated 10,000 uniformed police, as well as 3,000 plainclothes officers have been placed around the city.
Beatrix announced her intention to step aside in January after more than 33 years on the throne. She succeeded her mother, Juliana, who abdicated in 1980.
ccp/ch (AP, dpa)