The private test was conducted in a laboratory in Edgbaston in England and Ajmal now needs to clear an official reassessment in an International Cricket Council (ICC) accredited laboratory in Chennai, India on January 24.
The 37-year-old was suspended over illegal bowling action in September last year and last month withdrew from the World Cup to be held in Australia and New Zealand in February-March.
His withdrawal came after remedial work carried out under former Pakistan spinner Saqlain Mushtaq to alter his bowling action fell short.
"I cleared the private test," Ajmal told AFP. "The tests were conducted in Edgbaston and all my deliveries including the 'doosra' (his trademark swing) were within 15 degrees."
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Under the ICC rules all bowlers are allowed to straighten their bowling arm by 15 degrees, beyond which the action is deemed illegal.
Ajmal's first assessment in August last year revealed his arm extension went to 43 degrees.
Ajmal, however, remained unsure whether he would be able to feature in the World Cup or not.
"I want to do what is best for my country and for my team."
Pakistan Cricket Board chairman Shaharyar Khan on Tuesday ruled out Ajmal's participation in the World Cup, saying it was too late to consider it.
Ajmal was included in the preliminary 30-man squad for the World Cup, but after his withdrawal was dropped from the 15-man party announced last week.
However, under the ICC rules all teams can replace a player before the February 7 deadline, a week before the World Cup starts.