Colapinto is a member of the Williams Academy and made his FP1 debut at the British Grand Prix earlier this year.
He becomes the first Argentine driver in F1 in 23 years and just the second Argentine to drive for Williams after Carlos Reutemann.
"Colapinto will race with the team for the remainder of the 2024 FIA Formula 1 World Championship season and will compete from the Italian Grand Prix alongside Alex Albon. He will use the race number 43," Williams said in a statement.
Williams are ninth of the 10 teams, with only four points from 14 races - all scored by Albon.
Sargeant was set to leave at the end of the year. Ferrari's Carlos Sainz will race for Williams next season after signing a multi-year deal last month.
"To replace a driver mid-season is not a decision we have taken lightly, but we believe this gives Williams the best chance to compete for points over the remainder of the season," Team Principal James Vowles said.
"We have just brought a large upgrade to the car and need to maximise every points-scoring opportunity in a remarkably tight midfield battle.
"This is undoubtedly incredibly tough on Logan, who has given his all throughout his time with Williams, and we want to thank him for all his hard work and positive attitude."
