Hodgson arrived at Vicarage Road just 24 hours after Ranieri was sacked on Monday following Watford’s slump into the Premier League relegation zone last weekend.
“Watford FC is delighted to confirm the appointment of Roy Hodgson as the club’s manager,” a statement said.
“The ex-England national team boss is joined by his trusted assistant Ray Lewington, who managed the Hornets so admirably from 2002 until 2005.”
Hodgson left Crystal Palace at the end of last season, with many believing his exit would mark the end of a distinguished coaching career.
Instead, the 74-year-old will take charge of a sixth different Premier League club, with the task of ensuring Watford do not make an immediate return to the Championship.
“Best known for leading the Three Lions during a four-year spell which took in Euro 2012, World Cup 2014 and Euro 2016, Hodgson has also managed extensively at club level in England and across the world,” Watford’s statement added.
“Most notably in this country, he led Fulham to their highest ever Premier League finish and Europa League qualification, where the Cottagers knocked out the likes of Juventus, Wolfsburg and Hamburg on their way to the final, eventually losing to Atletico Madrid.”
Ranieri was sacked on Monday after a 3-0 home defeat against fellow strugglers Norwich left Watford 19th in the table, two points from safety.
The well-travelled Italian lasted only 14 games after replacing Xisco Munoz in October, winning just two of those.
Hodgson is the 15th permanent managerial appointment in just under 10 years since the Italian Pozzo family took control of the club, located on the outskirts of London.
And he already has experience of working for the Pozzos after a brief spell as Udinese boss in 2001.
Hodgson has a reputation for rescuing troubled clubs. He saved Fulham from relegation after his appointment in 2007 and a decade later took charge of a Palace side that had no points from their first four league games.
The veteran manager stepped away from his role at Selhurst Park in May after four seasons in charge of his boyhood club.
The former Inter Milan boss refused to be drawn on whether he was planning to retire at the time.
“It is a dangerous thing to start making bold statements about retirement and this is the end of me,” Hodgson said.
“I really don’t know. I am certainly not leaving Crystal Palace with the idea of putting myself back on the market and trying to get another job, I really am stepping down from the club and stepping away from football for a while but who knows what the future will be.”
Hodgson’s first match in charge of Watford will be a crucial away clash against bottom-of-the-table Burnley on February 5.