The Princesses, writing a joint letter in tribute to their grandmother, described the "tears and laughter, silences and chatter, hugs and loneliness, and a collective loss for you, our beloved Queen and our beloved Grannie".
Saying they were "so happy" to know she was now reunited with "Grandpa" the Duke of Edinburgh, they addressed her directly to tell her the tributes that had been paid since her death "would really make you smile".
The sisters are particularly close to one another, and have regularly spoken of their love for their late grandparents.
"We've not been able to put much into words since you left us all," they wrote, in a statement published by Buckingham Palace.
Read the full tribute below:
"We've not been able to put much into words since you left us all," the statement reads. "There have been tears and laughter, silences and chatter, hugs and loneliness, and a collective loss for you, our beloved Queen and our beloved Grannie."
They continue: "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.
"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.
"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."