But Driver fell two months short of the required five years of schooling.
Driver said: "We had to check with my old school and it then became apparent that I was short of the five years required. Nobody is to blame here."
Teenage Somali-born Celtic forward Islam Feruz became the first player to be selected for Scotland under the new schooling rule.
And Scotland coach Craig Levein had hoped that 22-year-old Driver would follow despite having been capped for England at the Under-21 European Championship last summer.
However, the Hearts winger - who played for Scotland schoolboys, once scoring against the land of his birth - told Hearts' website: "I am massively disappointed at the outcome, but these things cannot be helped.
"I was excited at the prospect of playing for Scotland and was very impressed by what Craig Levein had to say when the idea was first mentioned.
"I am a positive character and I just have to concentrate on getting myself fit and back into the Hearts team. We have a new manager in Jim Jefferies and I have a new challenge to make sure I am a part of his plans.
"It is disappointing to think that I may have had a chance of playing for Scotland in a European Championship qualification campaign, but there is no point in dwelling on that disappointment."
Injury has restricted Driver to just 11 appearances for Hearts this season, but Levein said last week that the player wished to be considered for selection once he returned to fitness.
However, the SFA said in a statement: "Upon investigation of Andrew Driver's eligibility by the Scottish FA, it has emerged that - despite widespread public belief since the inception of this new rule - the player does not, in fact, fulfil this criterion."
And Levein told the SFA website: "Firstly, let me express my heartfelt sympathy and deep disappointment for the player, who had expressed a keenness to play for Scotland when it first emerged he may have been eligible under the new rules.
"I spoke to the player and his father today to inform them and they were obviously and understandably disappointed.
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"I consider Andrew a fantastic player with a great future ahead of him and I would have been delighted to work with him at Scotland.
"This is not now possible, but I would ask everyone to allow Andrew the time and space to concentrate on his club career and I wish him all the best."
SFA chief executive Gordon Smith expressed his disappointment but said Scotland had to abide by the new rules.
"Since the Scottish FA was at the vanguard of amending the Fifa regulation, in order to place an emphasis on being educated in the country for a prolonged period and not simply being a continuous resident, it was imperative that we had to protect the ruling as agreed with the other Home Associations," he said.
"It is unfortunate that Andrew Driver is not eligible, but I would rather this was determined now rather than at a later juncture that could have had serious implications for the Scottish FA or the results of the national team."
Hearts manager Jim Jefferies said Driver must now focus on playing for Hearts "and getting a game for England".
Source: BBC Sport