Nielsen, who will be responsible for Williams' overall management and operation of sporting matters, joins from Toro Rosso where he had been sporting director since 2013.
The 50-year-old has also spent time as team manager at Tyrrell and Arrows and as sporting director at Benetton/Renault and Caterham during his 27 years in Formula One.
"In this role I will be able to help ensure that our operations at the race track are maintaining the highest standards and that we are maximising our performance at the race track from a sporting perspective," Nielsen said in a statement.
Williams enjoyed a successful 2014 season, finishing third in the constructors championship behind Red Bull and winners Mercedes.
(Reporting By Michael Hann. Editing by Patrick Johnston)
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