The monarch received the gift from the Royal Horticultural Society (RHS) and watched it placed in the Windsor Castle gardens last week to commemorate Philip's centenary on Thursday.
The Queen described the Duke of Edinburgh Rose, which is deep pink, dappled with white lines and double-flowered, as "lovely" and the tribute as "very kind".
Receiving the gift on Wednesday, the Queen was wearing sunglasses in the June sunshine and dressed in a summery blue dress with a white floral pattern, white cardigan and a string of pearls, and was holding a patterned silk scarf.
RHS president Keith Weed told the Queen: "It's a rose named the Duke of Edinburgh Rose to mark his centenary and it's a commemorative rose for all the marvellous things that he did over his lifetime and for everyone to remember so much that he did.
"Each rose, there's a donation that goes to the Living Legacy Fund which will help more children. It's a beautiful flower in itself, a double flower."
The Queen said: "It looks lovely."
The Duke of Edinburgh Rose was newly bred following Philip's death on April 9 by Harkness Roses, which has been breeding and growing British roses since 1879.
For every rose sold, the firm will donate £2.50 to The Duke of Edinburgh's Award Living Legacy Fund, which will help one million more young people from all backgrounds and circumstances take part in the youth award scheme set up by Philip in 1956.
The Duke of Edinburgh Rose is described as having a delicate fragrance, and its flowers will develop in large clusters on long stems.
Mr Weed said: "Whilst being very poignant, it was also a delight to give Her Majesty The Queen, patron of the Royal Horticultural Society, the Duke of Edinburgh Rose to mark what would have been HRH The Duke of Edinburgh's 100th birthday and to remember his remarkable life."
Prince Philip, who was born on June 10 in 1921, was the nation's longest serving consort and dedicated decades of his life to royal service.