The American youngster joins the programme following a campaign which saw him finish seventh in the F3 championship with four podiums and victory.
“It's a team with not only a fantastic history, but a great track record of bringing young talent into Formula 1.
“I am really excited to begin working with the team and can't wait to hit the ground running.”
Williams team boss Jost Capito added: “I am incredibly pleased to welcome Logan to the Williams Racing Driver Academy.
“He's demonstrated his talent in FIA Formula 3, consistently delivering strong results in an extremely competitive field.
“I'm proud that Williams will play a part in supporting the progression and growth of another talented young driver.”
Sargeant's role within the Academy will see him in action in the team's simulator and work alongside the team both trackside and at its Grove factory.
The 20-year-old has three years of FIA Formula 3 Championship experience behind him, finishing third in 2020 behind Australian championship winner Oscar Piastri.
He had been slated to test for IndyCar team AJ Foyt Racing at Barber Motorsports Park on Monday, though it was revealed by the team on Thursday that it would not progress with that outing.
In August, Williams parted ways with Dan Ticktum, the 22-year-old Brit released from the Williams academy for unspecified reasons.
The squad, now owned by American investment firm Dorilton Capital, still has Roy Nissany, Jack Aitken, and Jamie Chadwick on its books.
Sargeant's own 2022 racing programme is yet to be confirmed.