The Florida-born driver, currently third in the Formula Two series, and made his F1 race weekend debut when he took part in the first free practice for the US Grand Prix in Austin on Friday.
All going to plan, he will become the first American to race in Formula One since Alexander Rossi entered five Grand Prix with now-defunct Marussia in 2015.
"We feel he is ready to race and under the condition that he has enough super-license points after (the season-ending race in) Abu Dhabi he will be our second driver next year," Williams team principal Jost Capito told reporters on Saturday.
"We believe he is absolutely ready to get into Formula One," he added.
Capito said Sargeant had performed as expected and done exactly what he was told to do in practice.
"He had one season in F2 and I'm a fan of getting young drivers as quickly through as possible to Formula One," he said. "Get him in as quick as possible and find out if he is capable to stay in Formula One a long time, which we believe he is."
Sargeant will replace Canadian Nicholas Latifi in the team, who are currently last in the standings, alongside experienced British-born Thai Alex Albon.
Williams, who are owned by US-based private investment firm Dorilton Capital, said Sargeant would also take part in Friday practice in Mexico City next week and Abu Dhabi on November 18th to boost his super-license points tally.
He is also carrying out private testing and extensive simulator work.
The Formula Two title has been won already by Brazilian Felipe Drugovich but Sargeant has won two races. He is in third place, nine points clear of Australian Jack Doohan, Indian Jehan Daruvala, and Brazilian Enzo Fittipaldi with one round remaining.
Formula One will have three races in the United States next season, with Las Vegas making its debut in addition to Miami and Austin, and having a local driver has been seen as the next important step.
"I think it's great news and congrats to Jost and the Williams team in hopefully achieving that," said Red Bull boss Christian Horner, who recently tried to sign American Colton Herta for Red Bull's AlphaTauri team.
That attempt failed due to multiple IndyCar race winner Herta lacking a super-license and the governing FIA refusing to bend the rules.
"We see the growth in the US, we see the excitement that there is... you can see the American public are really engaged in Formula One," added Horner.
"I think we need an American driver and not just a driver but a successful driver competing in there as well, and it shouldn't just be Brad Pitt."
Hollywood actor Pitt is set to star in a Formula One movie and briefed the team bosses and F1 executives on developments at the Austin track on Friday.
Williams's move for Sargeant leaves US-owned Haas as the only team still with a possible vacancy as they decide whether to retain German Mick Schumacher or replace him.
Follow all the action in the US Grand Prix from Austin on Flashscore.
