No one comedian has been credited with that line, but it is reported that the phrase came from the comedy circuit that sprung up after World War II to replace the final demise of Vaudeville (skip down for the short answer).
The comedy circuit ran primarily at dinner clubs and resort hotels in and around the New York area. There were 400 odd establishments that comedians, musicians and other entertainers could play in that mountain region alone. Several famous comedians go their start or worked there for a period such as Milton Berle, George Burns, Red Buttons, Norm Crosby, Jerry Lewis, Buddy Hackett, Pat Cooper, Freddie Roman, Jonthan Winters and Bill Dana.
Short answer: the phrase arose due to the fact that the popular thing to do at the end of a comedian’s act was to plug himself and the establishment in which he was playing.