Between 2004 and 2006 Klien raced for Jaguar, staying on when the team was taken over by Red Bull.
Klien was replaced by Vitantonio Liuzzi for the next three races but the rules prevented him from driving in practice.
"I'd like to thank Spyker for this opportunity, " said Klien, who lost his Red Bull seat to Mark Webber in 2007.
BBC: SPORT | Motorsport | Formula One | Spyker hand Klien testing drive
But now Klien will be able to test on the Friday of San Marino, Spain and Monaco before possibly resuming racing.
Red Bull argued that other teams such as McLaren have used third drivers with far more F1 experience than the 22-year-old Klien.
More positively, analysts said that Mr Klien's departure from the firm suggested that an imminent departure of chief executive Steve Ballmer was unlikely.
Klien, 27, has raced in F1 for both Jaguar and Red Bull and has been a test driver for Honda and BMW Sauber.
Klien, 23, is a test driver for Honda but the team have given him permission to drive for Spyker in Spa on Thursday.
BBC: SPORT | Motorsport | Formula One | Spyker hand Klien testing drive
Kolles said Austrian Christian Klien and Japan's Sakon Yamamoto, who both raced for Hispania last year, remained in the frame along with others.
BBC: Bruno Senna out of the running for Hispania second seat
"This role offers me the opportunity to rejoin the Formula 1 environment and drive again, which is naturally where my longer-term ambitions lie, " said Klien.
Klien, who will take part in a race weekend for the first time since the 2007 British Grand Prix when he replaced Jenson Button in second practice at Silverstone while at Honda, is eager to impress his new boss.
The driver line-up is not yet known, but Austrian Christian Klien, who got the Jaguar seat last season due to his Red Bull sponsorship, and Italian youngster Vitantonio Liuzzi, who Red Bull backed to the Formula 3000 title this season, are among the candidates.
BBC: SPORT | Motorsport | Formula One | Red Bull snaps up Jaguar F1 team
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