Solskjaer, who was appointed United's permanent manager in March 2018 after a highly-successful three months in interim charge, leaves Old Trafford with the club seventh in the league standings, 12 points behind leaders Chelsea having lost five of their last seven matches.
"Manchester United announces that Ole Gunnar Solskjaer has left his role as manager," the club said in a statement. Ole will always be a legend at Manchester United and it is with regret that we have reached this difficult decision.
"While the past few weeks have been disappointing, they should not obscure all the work he has done over the past three years to rebuild the foundations for long-term success. Ole leaves with our sincerest thanks for his tireless efforts as Manager and our very best wishes for the future.
"His place in the club’s history will always be secure, not just for his story as a player, but as a great man and a Manager who gave us many great moments. He will forever be welcome back at Old Trafford as part of the Manchester United family."
The defeat at Vicarage Road proved to be the final straw and it was reported that the United board had conducted an emergency meeting on Saturday night to decide the Norwegian's fate. United co-chairman Joel Glazer is understood to have approved and rubber-stamped the decision.
After comprehensive defeats to rivals Liverpool and Manchester City, United sunk to a new low at Watford, and goalkeeper David De Gea described the team's performance as a "nightmare".
"It was embarrassing, the way we played today," De Gea told BBC Sport. "The first half was very poor - it's not acceptable for this club and the level of players that we have. It's another nightmare. There's been some difficulties but I don't really know what to say."
Solskjaer, 48, failed to win any silverware during his two full seasons in charge, although United did reach last season's Europa League final where they lost on penalties to Villarreal.
The Norwegian guided United to a runner-up finish in the Premier League in May, but despite the expensive and high-profile summer signings of Cristiano Ronaldo, Jadon Sancho, and Raphael Varane, the team has dramatically regressed.
Solskjaer is a legendary figure at Old Trafford thanks to his exemplary nine-year spell as a player, collecting six Premier League winners' medals and two FA Cups, while he was responsible for one of the most famous moments in the club's history when he scored the injury-time winner against Bayern Munich in the 1999 Champions League final.
Michael Carrick has been placed in temporary charge of the first team, United confirmed, as the club "looks to appoint an interim manager to the end of the season".