The FA reportedly wrote to the Scottish, Welsh and Northern Irish associations on Monday to inform them of the decision after failing to gain their support.
FIFA had confirmed that all four home nations would have to support a Team GB, and the Football Association of Wales especially has been vehemently opposed to the idea.
The FA wrote to the Scottish, Welsh and Northern Irish associations in January telling them of its intent to enter men's and women's teams for Rio, but Britain's FIFA vice-president Jim Boyce confirmed earlier this month all home nations would have to consent.
Boyce said: ''I was given an absolute categorical reassurance from FIFA that unless full agreement could be reached between England, Scotland, Wales and Northern Ireland, there would be no GB team participating at next year's Olympics.''
WHAT SOCIAL MEDIA SAID
It was romantic to have two British football teams competing on home soil at London 2012. Now, other time, however, it makes no logical sense. The 2012 event was a one-off and it is correct to remain as such.
Apart from anything else, the GB team at the 2012 Games looked like exactly what it was: a group of players thrown together at the last minute in order to fly the flag. Up against cohesive, well-drilled U23 sides from around the world - sides full of players who'd been together for years, coming through their various youth systems - it was no surprise that Britain's players had little or no cohesion in their play. Sure, it was fun as a one-off - but it's best left at that. When Glasgow hosts the Games in 2058 perhaps we can revisit the idea - but it's probably best left on ice until then.
WHAT HAPPENS NEXT
Well that appears to be the death knell for an Olympic GB football team. While much of the focus is on the men’s team, this decision also means that there will be no women’s team at Rio either.