Hodgson was announced as the club’s new manager on Tuesday evening following the departure of Claudio Ranieri after only 16 weeks in charge.
The 74-year-old will be joined at Vicarage Road by assistant Ray Lewington, who managed the Hornets from 2002 until 2005.
Hodgson becomes the Hornets’ 15th permanent manager in the last 10 years, and the third boss this season after Xisco Munoz was dismissed in October.
Having left Crystal Palace at the end of last season after another campaign safely in the top flight, Hodgson now inherits a relegation-threatened team sitting 19th.
Watford were beaten 3-0 at home by relegation rivals Norwich last Friday night and are two points from safety, with their next Premier League match at bottom club Burnley on February 5.
“It’s a massive challenge, but it’s a challenge I believe I’m ready to take on and one that I’m very excited about,” Hodgson said on Watford’s official website.
“I’m certainly looking forward to it, and if the players are as good as I think they can be, then I’m hopeful of helping the club to another season in the Premier League.
“I’m confident in the sense that I’ve been in situations that aren’t so different to this before, at Fulham, West Brom and Palace.
“The period of time I had to change things might have been a bit longer on each occasion – and at West Brom the league position wasn’t as bleak – but in terms of coming in, getting my ideas across and getting the team playing, it feels somewhat similar.
“It’s going to be a difficult job for Ray and I, as I’m sure it would be for anybody, but I feel we’ve got the ability to be successful.
“I can certainly assure all the Watford fans that our desire to keep the club in the league will be every bit as great as theirs, and we’ll do everything we can to make that happen.”
Hodgson – in charge of England at the 2012 and 2016 European Championships as well as the 2014 World Cup – is not expecting things to be easy as he looks to get Watford back out of the bottom three.
“Every manager brings a new way of working and new ideas, and when you’ve only got a short period of time it can be tricky to really stamp that philosophy onto a group of players,” he said.
“It’s going to be a really intense four months for us, and if we are going to achieve our goal the players are the ones who are going to do it for us.
“I agree with the club’s belief that there is a group of good players here, but they have to buy into our ideas and show commitment to the shirt.
“There are no easy games in the Premier League and if we do stay up it’ll be because they’ve listened to what we’ve said and found the performances to earn the points we need.”
The Hornets will be the sixth Premier League club which Hodgson has managed following spells with Blackburn, Fulham, West Brom, Liverpool and more recently his boyhood club Palace.
Hodgson has also previously worked for the Pozzo family, owners of Watford, during a short stint as Udinese boss in 2001.
“I think it was the right time for me to step aside at Palace after a long four years, but my passion for the game was never missing, even when I stopped,” Hodgson said.
“I haven’t been waking up in the morning pulling my hair out, but I’ve certainly never lost that itch or desire to get back to work.
“I haven’t actively sought another position, and the last thing on my mind when I watched Watford’s match against Norwich last week was that I could become the club’s manager.
“It’s come out of the blue, but very pleasantly out of the blue and I do feel very ready to take this challenge on.”
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