Yoon declared martial law last Tuesday, deploying troops to the National Assembly and National Election Commission, before canceling the measure six hours later after parliament voted against it.
The independent investigation bill passed with 210 lawmakers voting in favor, 63 against and 14 abstaining from the 287 present.
Unlike regular special counsel investigations, a permanent prosecutor can proceed without presidential approval.
The probe will also target Prime Minister Han Duck-soo and former ruling People Power Party (PPP) floor leader Choo Kyung-ho.
Investigators will also look into former martial law commander Gen. Park An-su and Defense Counterintelligence Command chief Yeo In-hyeong, who allegedly helped plan the martial law decree.
The PPP allowed its lawmakers to vote on their own on the bill introduced by the opposition Democratic Party.
The legislation cleared a parliamentary committee Tuesday after PPP members boycotted the session.
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