A wikipedia search gave me the following information:
Competition from television drew audiences away from movie theaters in the late 1950s, and the theatrical cartoon began its decline. Today, animated cartoons are produced mostly for television.
American television animation of the 1950s featured quite limited animation styles, highlighted by the work of Jay Ward on Crusader Rabbit. Chuck Jones coined the term "illustrated radio" to refer to the shoddy style of most television cartoons that depended more on their soundtracks than visuals. Other notable 1950s programs include UPA's Gerald McBoing Boing, Hanna-Barbera's Huckleberry Hound and Quick Draw McGraw, and rebroadcast of many classic theatrical cartoons from Warner Brothers, MGM, and Disney.
The Hanna-Barbera cartoon, The Flintstones, was the first successful primetime animated series in the United States, running from 1960-66 (and in reruns since).
And in case you want to know first cartoon to be broadcasted on TV, here is it:
The WALT DISNEY cartoon Donald's Cousin Gus was the first film cartoon shown on the May 19, 1939 telecast of NBC's experimental station W2XBS (now WNBC) in New York.
Another useful reference in this regard: