John D. Backe has resigned as president and chief executive officer of CBS Inc., effective immediately, the corporation announced yesterday.

No reason was given for his resignation.

Backe has been president of CBS since 1976, when chairman William S. Paley suddenly dismissed Arthur R. Taylor, who up to that time had been Paley's heir apparent. Backe had come to the post from the corporation's publications department. Just before his promotion, he helped to engineer the acquisition of Fawcett Publications.

In a recent interview, Paley praised Backe generously and suggested that here, at last, was his successor.

At the time Backe assumed the chief executive spot, people within the corporation doubted whether, despite his assertions to the contrary, Paley would not continue to have the final say. Dennis Leibowitz, broadcast analyst with E. F. Hutton, said in 1977: "There is no way to prove it or disprove it, but especially after what happened to Mr. Taylor, no one, I think, believes that Mr. Paley could not still make unilateral, spur-of-the-moment decisions."

In a statement, CBS said that until Backe's successor is chosen, the chief executive function at CBS will be exercised by the office of the chairman, consisting of Paley; John R. Purcell, executive vice president; Gene R. Jankowski, president of the CBS Broadcast Group; and Walter R. Yetnikoff, president of the CBS Records Group.

CBS Inc. is composed of four "groups," of which the Broadcasting Group is the largest, accounting for $1.8 billion out of $3.5 billion total revenues. The other groups are publishing, records and the Columbia Group, which includes miscellaneous business operations such as the record club, toys and musical instruments.