Hodgson, 74, takes over from Claudio Ranieri, who was sacked on Tuesday (AEDT) after just three months in the role.
Ray Lewington, who was Watford boss from 2002 to 2005 and has worked extensively as Hodgson's assistant manager, has also joined the club.
Hodgson's coaching career stretches back to 1976, when he took charge of Swedish side Halmstad for four years.
The work has already begun 👊 pic.twitter.com/3fVW84Muay— Watford Football Club (@WatfordFC) January 25, 2022
His club career has seen him manage teams ranging from Inter, Liverpool and Udinese to Blackburn Rovers and Neuchatel Xamax, while he has also coached the national teams of Switzerland, the United Arab Emirates and Finland.
A fan favourite at Fulham after leading them to the Europa League final in 2010, Hodgson became England boss two years later, reaching the quarter-finals of Euro 2012.
His Three Lions tenure proved disappointing on the big stage, though, with England exiting the 2014 World Cup at the group stage before being knocked out of Euro 2016 by Iceland, after which he left the role.
A four-year spell back in the Premier League with Crystal Palace followed, with Hodgson ensuring their survival after they lost the first seven games of the 2017-18 season before guiding them to 49 points in 2018-19, equalling their best ever tally.