After the war he was again elected to the Massachusetts House, serving four terms, 1947 to 1955, and attaining the position of assistant majority leader.
In 1958 Burke was elected to the Eighty-sixth Congress. He was reelected to the nine succeeding Congresses, and served from January 3, 1959, to January 3, 1979. He rose through seniority to become the second-ranking Democrat on the Ways and Means Committee, and was considered an expert on the Social Security system. Burke was not a candidate for reelection in 1978 to the Ninety-sixth Congress.