The 74-year-old was appointed on a short-term deal in January to replace Claudio Ranieri, but he has been unable to pull the Hornets away from relegation trouble.
Hodgson has so far taken charge of 14 games since arriving, winning two, drawing two and losing 10, including each of their last five outings.
Watford's relegation from the Premier League will be confirmed on Sunday should it fail to beat Hodgson's previous employer, Crystal Palace.
The former Liverpool and England manager said he explained to the club's board that he was only ever interested in a short-term deal and so will leave Vicarage Road once the campaign concludes.
"Obviously, it's a short-term [deal]," he said. "Certainly, I made it clear [to the board] it would need to be a short-term one between now and the end of the season. I took that job on and came out of retirement to do that particular job.
"Now that job has unfortunately ended. I've enjoyed my time doing the job. I don't think I shall be putting my name forward anymore for further sorties in the world of Premier League football. It's a very demanding world and I think I've earnt the right to step back and enjoy some free time and spend some time with my wife and son."
While Hodgson indicated this would be his last job in football, he did say the same after leaving Palace at the end of last season, before answering Watford's call, and admitted "itchy feet" could see him return, though not at the top level.
"I don't think we'll ever lose that [itchy feet]," he added. "I think you can speak to any other managers that have actually decided to step aside and announce their retirement, but they still do something within the game.
"I'd like to think that I'm always going to be passionate enough about the game and involved enough in the game that some particular aspect of work might come my way which I think I can happily do but as I say, it's not something I'm punting for.
"It certainly won't be in charge of a [Premier League] team. I think that's my swansong on that one."
Hodgson was at Buckingham Palace to receive a CBE from Prince William for his services to football.