Fred Silverman has resigned as president and chief executive officer of the National Broadcasting Co., and Grant Tinker, until yesterday president of MTM Enterprises in Hollywood, has been chosen to succeed him and has been handed the difficult assignment of saving NBC.

To Tinker, 55, falls the task of reviving NBC from its slumbering last place in network ratings -- a position it held before and thoughout Silverman's three-year regime -- and boosting profits that dropped from $150 million in 1977 to $80 million, a third of those of rivals ABC and CBS, last year.

Thornton F. Bradshaw, who today takes office as chairman of parent corporation RCA, announced the shake-up yesterday in a five-minute closed-circuit telecast to NBC affiliates. "No one has ever worked harder or given of himself to his job more then Fred Silverman," said Bradshaw, reading haltingly from a teleprompter.But Bradshaw said Silverman, 43, had asked for "a statement of unequivocal support from me" after it was announced that Bradshaw was replacing Edgar Griffiths as RCA chairman, and "I was not prepared to make that type of commitment."

Bradshaw said Tinker -- whose production company has given birth to such highly regarded TV hits as "Lou Grant" "Rhoda" and "The Mary Tyler Moore Show," which starred Tinker's ex-wife -- was "one of television's ablest executives, a skilled administrator adept at motivating creative talents." Bradshaw said he met Tinker for the first time on May 20 and soon found him "receptive to a larger challenge that could climax his long and successful career."

It is a larger challenge indeed. NBC is in last place in prime-time and daytime ratings; its news division is not only an also-ran to front-runner CBS but now finds itself challenged by an aggressive ABC News under the leadership of Roone Arledge. Morale at the network is said by one to be as droopy as its profits.

Tinker was named "chairman and chief executive officer" of NBC; Bradshaw said a new president of the company would be named later after consultation with Tinker. Bradshaw also took the unusual step of nominating Tinker to the board of directors of RCA, a policy not followed at the company in recent years.

NBC also released a farewell letter from Fred Silverman, on vacation in Hawaii, in which Silverman said he resigned when Bradshaw failed to express the requested support. Silverman predicted eventual success for NBC and said "I will take pride in that accomplishment because I feel I have laid the foundations for that progress."

Lee Solters, a spokesman for Silverman, said the fabled programmer had no plans beyond extending his vacation and said he told Solters by phone from Hawaii, "I'm greatly relieved" at the turn of events.

A spokesman for MTM said from Hollywood that Tinker's resignation as president had been accepted and that Mary Tyler Moore would retain her position as chairman of the board.Tinker, now vacationing in France, is expected back in the United States on July 7.

An MTM source said Tinker had twice before been offered the presidency of NBC, prior to the Silverman era, and declined it. Bradshaw, asked yesterday what persuasion he had used to get Tinker to change his mind, said, "I just think he's a man who likes a challenge."

Asked if Tinker would receive an annual salary at least as high as Silverman's $1 million, Bradshaw declined to cite a figure but said the new salary "has little relation to what he has been making at MTM." Bradshaw said he did not give Tinker a timetable for making NBC No. 1 in ratings for raising profits.

"I don't talk in those terms," Bradshaw said. "No. 1 by Christmas' is not good terms to talk in. This is a commercial venture, and it should make considerably more money than it does make. Compared to the other networks, it falls short." As for a timetable, "I'll know when he's making the right kinds of moves in terms of the way he runs the business."

Bradshaw confirmed a network insider's report that Tinker will be headquarted not in New York but in Los Angeles, leaving the president of the company, still to be named, to handle administrative matters in New York. "Grant Tinker will retain responsibility for all decisions, but he will not be making all decisions," said Bradshaw. Was this a reference to Silverman's reputed reluctance to delegate authority? "Fred did spread himself," said Bradshaw.

In an obvious move to establish a vigorous take-charge aura from the first moments of his tenure. Bradshaw also confirmed reports yesterday that "my friend Tom Brokaw," currently host of the "Today Show," had signed a new contract with NBC News. Details, to be made official at a press conference at the 21 Club in New York today, have Brokaw moving to the "NBC Nightly News" next April as co-anchor with Roger Mudd, currently "chief Washington correspondent."

John Chancellor, now the sole anchor of the broadcast, will move into an Eric Sevareid-like commentator role, appearing three or four times a week. Chancellor said yesterday that stepping down as anchor was not a punishment but a reward.

"This is not a situation where I wanted to hang on as anchorman," Chancellor said. "Ask my friend of mine and you'll find that's true. It was built into my last contract that I go into this new role. It is what I ultimately want to do in broadcasting."

Chancellor did concede that the timing of the announcement was affected by NBC's -- and Bradshaw's -- intense desire not to lose Brokaw, who had been noisily considering an offer from Arledge and would have been adding to the anchor team of ABC's "World News Tonight" in the twinkling of an eye.

According to a highly placed NBC source, Brokaw was close to signing with NBC on Monday but held out for top billing on the revamped newscast. And he got it: "NBC Nightly News with Tom Brokaw and Roger Mudd."

Brokaw's departure from "Today" provoked immediate speculation about his successor there. Network insiders say the top candidate is reporter Chris Wallace, 33, who has frequently filled in for Brokaw during vacations. Wallace said yesterday that he has not been approached about the job but indicated extreme interest, calling it "a very exciting thing to do in journalism" and "a remarkable opportunity."