U.S. District Court Judge George J. Mitchell, 46, today was named by Gov. Joseph E. Brennan to succeed his longtime political ally Edmund S. Muskie in the Senate.

Mitchell will serve out the remainer of Muskie's term, which expires in 1982, after which, he said, he will run for election to a full, six-year term.

At a news conference following the announcement of his appointment, Mitchell said he plans to conclude his court business "within the next few days" and take over the Senate seat.

Asked if he was overwhelmed by stepping into the shoes of Muskie, a two-decade Senate member who is the new secretary of state, Mitchell replied: t"Well, since I am here it obviously didn't overwhelm me."

Mitchell said it would be presumptuous of him to play a role in the party's selection of a presidential nominee or to try to influence the selection process because "it is drawing to a close."

He said he would vigorously support construction of the controversial Dickey-Lincoln hydroelectric power project in northern Maine, which has had Muskie's strong backing but which had been opposed by the other members of Maine's congressional delegation, all of whom are Republicans.

While Mithcell's appointment was lauded by state Democratic leaders, former U.S. senator William D. Hathaway said he "was very disppointed I didn't get it myself, and disappointed in the choice of Mitchell."

Hathaway, who gained prominence when he defeated incumbent Margaret Chase Smith to win his Senate seat in 1972, was defeated for reelection by Republican William S. Cohen in 1978.

"I think because of my experience I should have been the first choice," Hathaway told Associated Press. "I could do more for the state and step into the role without any breaking in."

Mitchell, who has never held elective office, has long been involved in politics, and has been tied closely to Muskie since 1962, when he served as his executive assistant.

He was Muskie's deputy campaign director when the Maine senator was the Democratic vice presidential candidate in 1968 and held the same post four years later when Muskie unsuccessfully sought the presidential nomination.

The son of a utility company laborer who later worked as a janitor at Colby College in Waterville, and a Lebanese immigrant mother who for 27 years worked the midnight shift at a Waterville woolen mill, Mitchell was graduated from Bowdoin College in 1954. After two years as an Army intelligence officer, he enrolled at Georgetown University Law School, attending evening classes while working as an insurance adjuster to pay his way through school. Mitchell joined Muskie's staff as an executive assistant after a brief stint with the antitrust division of the Justice Department.

He was elected Maine's Democratic state chairman in 1966. In 1974, he was defeated in the race for governor by independent James B. Longley.

In 1977 was appointed to be the U.S. attorney for Maine, a post he held for two years when he was named to the newly created federal judgeship in Bangor.