In a picture posted by Twitter user, Rodrigo, the letter is set out in beautiful simplicity with black borders around the message.
At the header is Anne’s royal insignia accompanied with the message.
Returning to royal duties over the last week, Anne and her husband vice-admiral Sir Tim Laurence attended a war memorial service on Sunday.
The pair marked the Anzac Day service by laying a wreath in tribute to the spirit and courage of the Australian and New Zealand forces who lost their lives.
Accompanied by her husband, Anne laid a wreath at Wellington Arch before visiting Westminster Abbey for the service.
Prince William also sent a letter praising the qualities of the New Zealand and Australian troops in a letter to both High Commissions.
He said: “This Anzac Day, Catherine and I join Australians and New Zealanders across the world to remember and honour the servicemen and women of the Australian and New Zealand Army Corps.
Following her father’s funeral, Anne, often regarded as one of the hardest-working royals, travelled to the Isle of Wight to conduct royal duties.
Wearing all black, the Princess Royal travelled to visit the Royal Yacht Squadron in Cowes.
In a touching statement, Anne spoke of her sorrow at losing her father.
In the statement, she revealed Philip had been her greatest supporter but also the person she wants to emulate.
She said: “You know it’s going to happen but you are never really ready.
“It is his example of a life well-lived and service freely given that I most wanted to emulate.