The final tally - 50 to 48. Voting took place on Saturday afternoon.
President Trump's nominee faced a storm of opposition when three women claimed Kavanaugh had sexually assaulted them, or other women, decades ago.
Heckling broke out repeatedly in the gallery as the vote was taken.
Some people were heard shouting "shame on you," briefly delaying the proceedings until order was restored.
Kavanaugh will become the 114th Supreme Court justice in United States history.