WASHINGTON, June 15— Grace Tully, a personal secretary to Franklin D. Roosevelt in his years as Governor of New York and as President of the United States, died today after a long illness. She was 83 years old.

Miss Tully, born in Bayonne, N.J., was a lifelong Democrat. She had lived in Washington since 1932, when she moved here after Roosevelt's election. Both in Albany and in Washington, she was a close friend and confidante of the Roosevelt family, frequently dining with them at the White House and accompanying them on picnics, fishing outings and weekends at Shangri-la, the retreat now known as Camp David, as well as official trips.

Miss Tully was one of several members of the White House staff who were with Roosevelt on his last visit to the Little White House in Warm Springs, Ga., where he died April 12, 1945.

In her book of memoirs, ''F.D.R. - My Boss,'' published in 1949, Miss Tully told of arriving at the Roosevelt cottage that afternoon and being told by doctors that the President had died. 'Wordless and Tearless'

''Without a word or glance toward the others present,'' she wrote, ''I walked into the bedroom, leaned over and kissed the President lightly on the forehead. Then I walked out on the porch and stood wordless and tearless. In my heart were prayers and, finally, in my mind came thoughts, a flood of them drawn from 17 years of acquaintance, close association and reverent admiration.''

Miss Tully had occupied a front row seat at momentous events as secretary and friend to the man she called ''the Boss.''

To her, he had dictated letters to kings and to generals, manuscripts for his radio fireside chats and such historic speeches as the one he delivered to Congress on Dec. 8, 1941, asking for a declaration of war against Japan.

In her memoirs, she told of being called to his office late in the afternoon of Dec. 7, only hours after the Japanese had bombed Pearl Harbor. Roosevelt Dictated Calmly

''He was alone, seated before his desk on which were two or three neat piles of notes containing the information of the past two hours,'' Miss Tully wrote. ''The telephone was close by his hand. He was wearing a gray sack jacket and was lighting a cigarette as I entered the room. He took a deep drag and addressed me calmly:

'' 'Sit down, Grace. I'm going before Congress tomorrow. I'd like to dictate my message. It will be short.' ''

And with that, she wrote, he began dictating as calmly as if he were merely answering a letter, specifying each punctuation mark:

'' 'Yesterday comma December 7 comma 1941 dash a day which will live in infamy dash the United States of America was suddenly and deliberately attacked by naval and air forces of the Empire of Japan period paragraph.' ''

The first draft of Roosevelt's speech, however, did not contain the ''live in infamy'' phrase. He dictated it as ''a date that will live in world history'' and later substituted ''infamy'' on the draft. It was then retyped as Miss Tully remembered it, and it was from that copy that he read the message to Congress. The reading copy of the message had been missing since it was delivered, but was recently rediscovered in the National Archives in Washington. The Lighter Moments

Miss Tully's book contained glimpses of other historic events she had witnessed, as well as lighter moments.

The President, she related, had a separation between two of his lower front teeth and a removable, single- tooth bridge had been fitted for the gap.

''He didn't particularly like to wear it,'' she wrote, ''and carried it most of the time in a tiny, heart-shaped silver box. With the tooth out, however, he whistled slightly on certain words and this extra sound effect was most noticeable on the radio. He forgot it on more than one occasion and quite often there was a mad last-minute dash by somebody from the Oval Room to his bedroom to rescue the little silver box from his bedside table.'''

Miss Tully was born Aug. 9, 1900, a family friend said. She attended a series of parochial schools, including St. Vincent's in Newark, Ladycliff-on-the-Hudson, Our Lady of Lourdes in Washington Heights and the Convent of the Holy Child before beginning secretarial training at the Grace Institute, operated by the Sisters of Charity. Eleanor Roosevelt's Staff

At the age of 18, she went to work for Bishop Patrick Hayes, who became Archbishop of New York and a cardinal. In 1928 she went to work for the Democratic National Committee office in New York City.

At first, she was assigned to Eleanor Roosevelt's staff, but soon was called upon to help Franklin Roosevelt after he entered the race for Governor of New York. After his election as Governor in 1928, she worked as an assistant to Roosevelt's longtime secretary, Marguerite LeHand. The two became close friends and were part of the extended Roosevelt ''family.''

In an interview several years ago, Miss Tully said: ''With the Roosevelts you weren't considered 'the help.' If you were working late, Mrs. Roosevelt would ask, 'Is that Tully's typewriter I hear?' And they'd put another chair at the dinner table.''

Miss Tully also worked for the Senate Democratic Policy Committee under the leadership of Senator Lyndon B. Johnson and of his successor, Senator Mike Mansfield. She joined the group in 1955 and retired at the end of 1965.

Survivors include a sister, Mrs. Paula Rolin Larrabee, and a niece, Alice L. Snoo Sinton, both of Washington. The family requests that contributions be made to St. Anne's Infant and Maternity Home, 4901 Eastern Avenue, Hyattsville, Md., or to a charity of the donor's choice. Services and burial are to be private.