The two bills are known together as the Community Safety Act and have been the subject of a heated debate in the past few months. Mayor Michael Bloomberg and Police Commissioner Raymond W. Kelly object to the measures, The New York Times said.
Both have warned the measures would hinder the police department and lead to a dangerous increase in crime.
Bloomberg issued a statement after the vote Thursday saying he would veto both measures.
One bill would create an independent inspector general to monitor and review police policy, conduct investigators and recommend changes to the department. The bill passed 40-11.
The other bill, which passed 34-17, would expand the definition of profiling to include age, gender, sexual orientation and housing status.
Bloomberg has 30 days to veto the bills, and if he does, the council then has 30 from its next meeting to hold an override vote.