In a message posted on the Royal Family’s Twitter account, Anne said it was her father’s example of a “life well lived and service freely given that I most wanted to emulate”.
With the message, she posted an image of herself and the Duke of Edinburgh laughing together at a sporting event.
The message read: “You know it’s going to happen but you are never really ready. My father has been my teacher, my supporter and my critic, but mostly it is his example of a life well lived and service freely given that I most wanted to emulate.”
It continued: “His ability to treat every person as an individual in their own right with their own skills comes through all the organisations with which he was involved.
“I regard it as an honour and a privilege to have been asked to follow in his footsteps and it has been a pleasure to have kept him in touch with their activities.
“I know how much he meant to them, in the UK, across the Commonwealth and in the wider world.”
She finished with the words: “I would like to emphasise how much the family appreciate the messages and memories of so many people whose lives he also touched.
“We will miss him but he leaves a legacy which can inspire us all.”
Anne is the Queen and Philip’s only daughter and the second of their four children.
She and her father shared a love of sport, particularly their passion for equestrianism.