The pair were among four simulator drivers named on Monday to work at the Italian team's Maranello factory in support of racers Sebastian Vettel and Charles Leclerc.
Wehrlein, who last year ended ties with Mercedes, drove for now-defunct Manor and Sauber in Formula One in 2016 and 2017 and the German is now racing for the Mahindra team in the all-electric Formula E series.
New Zealander Hartley, a two-times world endurance champion who won the Le Mans 24 Hours with Porsche in 2017, competed for Red Bull-owned Toro Rosso last year.
Italians Antonio Fuoco and Davide Rigon were the other two drivers appointed.
"Our team has taken on four undoubtedly talented drivers, who possess innate feeling, with a strong understanding of race cars and tracks," said team principal Mattia Binotto in a statement.
"These are exactly the qualities required in the skilful role of driving in a simulator, one of the vital pieces of equipment in the Formula One of today."
Russian Daniil Kvyat and Italian Antonio Giovinazzi, who performed simulator duties for Ferrari last year, are racing this season for Toro Rosso and Sauber respectively.
The season starts in Australia on March 17.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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