Hodgson, who has enjoyed an extensive and well-travelled career, with stints at the likes of Inter, Udinese and the Swiss national side, becomes the 18th manager in the Reds' history, after succeeding Rafael Benitez.
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The former Fulham boss, who guided the Cottagers to last season's Europa League final, was excited by the prospect of taking on a job he regards as one of the most attractive in football.
"This is the biggest job in club football and I'm honoured to be taking on the role of manager of Britain's most successful football club," he told his new club's official website.
"I look forward to meeting the players and the supporters and getting down to work at Melwood."
Hodgson is set to be officially unveiled by the club at a press conference this afternoon.
Fulham also confirmed that Hodgson had left his post at Craven Cottage and they wished him every succes in the future as they look to step up their search for a successor.
"Fulham confirm that at 9.20am this morning, Roy Hodgson resigned from his position of First Team Manager, effective immediately," a statement on the Cottagers' official website read.
"The club would like to wish Roy the very best for the future and thanks him for all that was achieved during his tenure.
"Ray Lewington will take temporary charge of team matters, until a successor is announced in due course."