NBC annouced officially yesterday the "resignation" of chairman Jane Cahill Pfeiffer, who earlier this week refused to quit her post and then was relieved of all responsibility by NBC President Fred Silverman.

In a quiet postscript to the acrimony and melodrama that marked statements and counter-statements on Tuesday, NBC said in a statement that Pfeiffer had resigned both as NBC chairman and as a board member of RCA, the parent corporation. Her contract, which was not to expire until October 1981, has been "settled" and "all outstanding issues . . . satisfactorily resolved," the statement said.

No dollar figures were released, but Pfeiffer's annual income was in excess of $400,000, and her settlement could well be in that area or beyond it.

The network also released an exchange of letters between Silverman and his onetime ally. Silverman's letter was short and semi-sweet: "Dear Jane: hI have valued the contribution you have made to NBC during the past two years. I wish you all success in your future endeavors. Sincerely, Fred Silverman."

Pfeiffer's was longer, and included a list of accomplishments she attributed to the team of Silverman and herself. That "the erosion of morale" within NBC News has been allegedly "turned around" was one of them.

"While the road has not been easy and our goals have not been fully achieved," Pfeiffer wrote, "I do believe NBC has the basic tools to be successful and to contribute to the industry. As I leave I have much affection for the people at NBC, and wish you well."

Reached at her home in Greenwich, Conn., yesterday, Pfeiffer said she did not want to comment beyond the statements and letters released by NBC. "Then it's all over?" she was asked. "It's all over," she replied.