Rose, 30, has signed a two-year deal at Vicarage Road after seeing a 14-year spell with Spurs come to a close when his contract expired at the end of last season.
The left-back, who has won 29 caps for England, spent his final season at Spurs training with the Under-23s, having been stripped of a squad number and left out of their Premier League squad by former manager Jose Mourinho.
Rose continues his rehabilitation from injury and it is not clear when he will be fully fit.
Watford have been looking for a left-back since January to provide competition for Adam Masina and targeted Rose before he joined Newcastle on a six-month loan in January 2020.
The Hornets have been busy in the transfer market since confirming their immediate return to the top flight, having already signed striker Ashley Fletcher on a free transfer, midfielder Imran Louza from Nantes and Rochdale's England youth international Kwadwo Baah from Rochdale.
Rose joined Spurs from Leeds United as a teenager in 2007 and made 214 appearances for the club, playing a key role in their run to the Champions League Final in 2019.
He strained relationships at the club with an explosive interview on the eve of the 2017-18 season, in which he took aim at Tottenham’s transfer policy, wage structure and ambition, telling Spurs to sign big names, "not players you have to Google and say, ‘Who’s that?’"
But on leaving the club, he said he would like to return after he finishes playing to work with their young players.
"I just had a meeting with the chairman [Daniel Levy] this morning," Rose said in an interview released by the club on June 4.
"He was asking me if I need any help with anything, said I'm welcome to come back in the future.
"I'm over the moon I did make that choice to come here in 2007 and I look forward to coming back after I've finished playing football and hopefully having an impact on the younger age group again, like I've had this season."
Spurs fans will have an early opportunity to give Rose a send-off next season, with Watford the visitors to the Tottenham Hotspur Stadium in the third round of matches, scheduled for August 28.