The former-Fulham boss was backed at a high of 18/1 with the online betting firm but quickly established himself as second favourite in the betting behind Harry Redknapp after some sustained support.
His first test as England boss will be against Norway in a Euro 2012 warm-up match on the 26 May before England's first match at the European Championships against France on Monday 11 June at the Donbass Stadium in Donetsk.
England are 11/8 to beat France in their opening Euro 2012 game but without their front man, Wayne Rooney, for the opening two games of the tournament they are 7/4 to be eliminated at the group stage.
Hodgson's side are 7/1 to end the tournament as runners-up and can be backed at 4/1 to leave the competition at the semi-final stage.
One of Hodgson's first duties as England manager will be to select a captain for the national side with Scott Parker the even money favourite to lead England out against France, Steven Gerrard is available at 6/4 with Manchester City goalkeeper, Joe Hart, in the betting at 7/1.
The new England manager is 20/1 to take Ben Foster, Chris Smalling and Bobby Zamora, three of his former players, to this summer's European Championships in Poland and Ukraine.