The Duchess of Cambridge's husband wrote to Fifa in his role as FA chairman to express his dismay that the team were not going to be allowed to wear the symbols in England's friendly against Spain.
Prime Minister David Cameron did the same, after earlier urging players to ignore the ban.
Hours after knowledge of the letters became public, Fifa changed their minds, and a compromise was reached.
The players will now wear poppies embroidered on black armbands. Images of poppies and messages of support will also be displayed prominently around Wembley and there will be a minutes silence before the match.
William, pictured below meeting with the prime minister and David Beckham in Zurich for the England 2018 bid, was delighted at the final decision.
St James's Palace said he was "happy at the victory for common sense."
A source added: "As a serving officer in the Armed Forces, who has lost friends and ancestors to conflict, William was particularly angered by the ban."
Second Lieutenant Joanna Dyer - a close pal of the Prince's from his Sandhurst days - was killed by a bomb in Iraq in 2007.
Major Alexis Roberts, lost his life in Afghanistan the same year. He was the Prince's Platoon Commander at Sandhurst and is remembered by his friend with "great fondness and respect".
Originally, Fifa had turned down the FA's request, saying: "We regret to inform you that accepting such initiatives would open the door to similar initiatives from all over the world, jeopardising the neutrality of football."
David Cameron called the ruling "outrageous". He said: "The idea that wearing a poppy to remember those who have given their lives for our freedom is a political act is absurd."