In March, the high court struck down the eavesdropping law, saying one of the nation's toughest measures was so broad that it could make videotaping a cheering crowd a crime.
The new law prohibits the secret recording of private conversations without consent from all parties. Law enforcement officials won the right for crimes for which authorities could use recording devices with the approval of a state's attorney.
Bill sponsors say the measure is a victory for privacy and free speech and doesn't curb the right to record police.
Quinn's office didn't offer an explanation for his Tuesday support.