Bookmaker William Hill slashed Redknapp's odds to 8/15 to take over the nation's team in time for the first Euro 2012 match against France, while Coral has stopped taking bets on Redknapp becoming the next England manager.
"We have taken fortunes all day on Redknapp becoming the next England boss after his success in the courts but the Capello news sent the betting on him into the stratosphere", said Coral spokesman Simon Clare.
Roy Hodgson, Stuart Pearce and Jose Mourinho were also linked with the job after Capello left his post with immediate effect.
Mr Bernstein said the resignation was the right course of action.
The FA chairman said: "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.
"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 had mixed success as an England manager, having left the nation disappointed with the team's fortunes at the 2010 South Africa World Cup.
Redknapp, meanwhile, has led Spurs trough the club's best era during the Premier League history.
Redknapp was at times moved to the verge of tears during his trial as the Crown alleged he told a pack of lies to get off the hook.
But jurors accepted Redknapp and Mandaric's evidence that the Monaco account in the name of Redknapp's dog, Rosie, was nothing to do with footballing matters at Portsmouth.