The 23-year-old was previously test and reserve driver for Force India, who now have Canadian owners and have been renamed Racing Point F1.
Williams, former champions who finished last in the championship that ended in November, have Britain's 2018 Formula Two champion George Russell and Poland's Robert Kubica as their race drivers for 2019.
British-based Williams said Latifi, whose father Michael this year bought a stake of around 10 percent in the McLaren Group, would help them at race weekends and in the factory.
He will drive in six Friday first free practise (FP1) sessions as well as test days before and during the season.
"It's a fantastic opportunity to continue my F1 development, and to build my on-track experience with more FP1 sessions and the rookie and Pirelli tests," said Latifi in a statement.
"As well as this, a big part of my role will be simulator driving and helping to support the development of the new car."
(Reporting by Alan Baldwin, editing by Christian Radnedge)
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