"We, like many, thought you'd be here forever. And we all miss you terribly.
"You were our matriarch, our guide, our loving hand on our backs leading us through this world. You taught us so much and we will cherish those lessons and memories forever."
The pair shared their fond memories of the Queen picking "heather and raspberries" for them, no doubt at her Balmoral Estate in Scotland, where the Queen died peacefully.
They continued: "For now dear Grannie, all we want to say is thank you. Thank you for making us laugh, for including us, for picking heather and raspberries, for marching soldiers, for our teas, for comfort, for joy. You, being you, will never know the impact you have had on our family and so many people around the world.
"The world mourns you and the tributes would really make you smile. They are all too true of the remarkable leader you are."
Beatrice, 34, and Eugenie, 32, said they were "so happy" their grandmother had been reunited with her late husband, Prince Philip.
And they said their uncle, King Charles, would continue to "lead in your example".
They added: "We're so happy you're back with Grandpa. Goodbye dear Grannie, it has been the honour of our lives to have been your granddaughters and we're so very proud of you.
We know that dear Uncle Charles, the King, will continue to lead in your example as he too has dedicated his life to service. God save the King. With our love."