The announcement was widely expected, especially in light of Robert Kubica's impending exit, and comes after Latifi took part in practice sessions and tests with Williams this year in his role as reserve driver.
The 24-year-old Canadian is currently second in the FIA Formula 2 Championship ahead of this weekend's final round, with four race wins over the campaign.
“I am thrilled to be stepping up as Race Driver for 2020,” said Latifi.
“I have thoroughly enjoyed working with the team this year, supporting them with the development of the car, and assisting wherever I can trackside and at the factory.
“I look forward to the journey ahead with the team, and I am excited to make my Formula One debut at the Australian Grand Prix in 2020.”
“All of us at Williams have been immensely impressed at what he has achieved this year in FIA Formula 2, along with his commitment to the team, and the work that he has put in behind the scenes.
“Nicholas has become an established and well-respected member of Williams, and we look forward to him stepping up into this new role, as we look to fight our way back to the midfield.”