The 29-year-old Briton replaces Germany's Adrian Sutil in the
role as back-up to race drivers Felipe Massa and Valtteri
Bottas.
Di Resta raced for three seasons in Formula One with the Force
India team between 2011 and 2013 with a best result of fourth
place.
"It will be a busy year combining both driving in DTM (German
Touring Cars) with Mercedes AMG, and attending the Formula One
Grands Prix in my new reserve driver role," said the Scot in a
statement.
"I will be giving my full support to both and look forward to
the exciting possibilities the year has ahead."
Mercedes-powered Williams finished third overall last season.
(Reporting by Alan Baldwin, editing by Patrick Johnston)
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