The discussions followed the FA decision to remove the England team captaincy from John Terry after the Chelsea defender's trial for allegedly racially abusing Queens Park Rangers' defender Anton Ferdinand was adjourned until July.
NEWS:Mumbling Capello never really settled
Terry, who would have led England at this year's European Championships, denies the charge.
"I thought it was right that Terry should keep the captain's armband," he said.
An FA statement said Capello's resignation had been accepted and he would leave his post immediately after just over four years in charge.
"I would like to stress that during today's meeting and throughout his time as England manager, Fabio has conducted himself in an extremely professional manner," Bernstein said in a statement.
"We have accepted Fabio's resignation, agreeing this is the right decision. We would like to thank Fabio for his work with the England team and wish him every success in the future."
Capello took over as England manager in January 2008 after England's failure to qualify for Euro 2008 under Steve McClaren.
Among those six, though, was a crushing 4-1 loss to Germany in the World Cup finals in South Africa 18 months ago. That was England's worst defeat in the finals and led to a chorus of calls for his dismissal.
Capello's tenure as England boss was a roller-coaster ride with several highs and lows. Apart from the World Cup, the lowest points both concerned Terry.
Terry was relieved of the England captain's armband after allegations that he had an extra-marital affair with the former girlfriend of his former Chelsea team-mate Wayne Bridge.
