"The FA welcomes FIFA's decision and thanks them for agreeing to this," the FA said in a statement.
"While continuing to adhere to the laws of the game, wearing the poppy on the armband does ensure the poppy will be visible throughout the game."
World football's governing body had initially rejected requests from the British government to allow England and Wales to wear poppies, instead permitting them to wear black armbands and observe periods of silence.
However, following statements from British Prime Minister David Cameron, who called the ban "outrageous" and "absurd", and FA president Prince William, FIFA changed its stance.
"The Duke's strong view is that the poppy is a universal symbol which has no political, religious or commercial connotations. The Duke has asked FIFA to apply an exception in this special circumstance," said a spokesman for Prince William, the Duke of Cambridge and second-in-line to the English throne.
England take on world champions Spain at Wembley and Wales play Norway in Cardiff on Saturday while Scotland are playing a friendly in Cyprus on Friday, and said with the Cypriot FA's approval they would do the same as England.
"The decision to allow players to wear black armbands featuring poppies during the match is a pragmatic solution to the fact that FIFA's rules forbid the wearing of the poppy on the match shirt," the Scottish Football Association (SFA) said.
"We believe this is a fitting way to show our respect for those members of the armed forces who have lost their lives fighting for their country."
British media confirmed that Wales would adopt the same addition to their kit for Saturday's match.
NATIONAL PRIDE
In a statement issued from his office earlier on Wednesday, Cameron said: "This seems outrageous. The idea that wearing a poppy to remember those who have given their lives for our freedom is a political act is absurd.
"Wearing a poppy is an act of huge respect and national pride. I hope FIFA will reconsider."
The British Government, backed by the English FA, HAD asked FIFA for permission to wear the poppies, the country's traditional way of remembering members of the armed forces who died in the line of duty.
Remembrance Day falls on November 11, the anniversary of the day the Armistice was signed marking the end of the First World War in 1918.
However, FIFA rejected the appeal in a letter to the FA.
"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," FIFA wrote.
FIFA had agreed to allow a minute's silence to be held before the games and for the teams to wear poppies on their training kits.
FIFA rules prevent items of a political nature being worn on shirts.
British sports minister Hugh Robertson wrote to the sport's world
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