Capello resigns as England manager
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.
Terry, who would have led England at this year's European Championships, denies the charge.
Capello, 65, expressed his unhappiness with the decision in an Italian television interview on Sunday.
"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."
A news conference with Bernstein has been scheduled for Wembley Stadium at 12:00 GMT on Thursday.
Capello took over as England manager in January 2008 after England's failure to qualify for Euro 2008 under Steve McClaren.
His first match, a friendly against Switzerland exactly four years ago this week, ended in a 2-1 victory and in he was in charge for 42 matches, winning 28, drawing eight and losing only six.
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.
He kept his job and guided England unbeaten through the qualifiers for the European Championships in Poland and Ukraine.
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.
Capello, who was on a salary of six million pounds a year, reinstated Terry last March. However, the latest incident proved one too many for the Italian and led directly to his resignation.
After winning 32 caps for his country, Capello enjoyed a glittering club management career.
He won four Serie A titles with Milan and one with AS Roma plus two La Liga titles with Real Madrid. He also took Juventus to two consecutive titles which were later stripped because of a match-fixing scandal.