President Carter completed his Cabinet shakeup yesterday by naming former New Orleans mayor Moon Landrieu to be the next secretary of housing and urban development and Portland, Ore., Mayor Neil E. Goldschmidt to be secretary of transportation.

The appointments were announced by White House press secretary Jody Powell, who said that Landrieu accepted the job Thursday and spent that night at the White House and that Goldschmidt agreed to join the administration during a meeting yesterday with the president.

Landrieu, 49, would succeed Patricia Roberts Harris, who is replacing ousted health, education and welfare secretary Joseph A. Califano Jr. Goldschmidt, 39, would succeed Brock Adams, who also was fired last week in Carter's purge of the Cabinet.

The appointments fill the last two major vacancies that were created by the shakeup. The White House still is assessing hundreds of subcabinet and middle-level White House aides, and there are likely to be changes in those positions in the coming weeks.

Harris' HEW nomination was confirmed yesterday by the Senate, which also confirmed W. Graham Claytor's nomination to deputy defense secretary.

Powell also announced yesterday that the president has invited all of the people he consulted during the Camp David "domestic summit conference" to join him for lunch at the White House Monday.

Powell said Carter wanted to thank those he consulted for their advice. He said the guests, numbering more than 130, also will be briefed by the president and other administration officials on the steps taken as a result of the Camp David summit and other measures Carter is planning to implement.

In announcing yesterday's appointments, Powell quoted the president as saying of Landrieu:

"Mayor Landrieu enjoys a national reputation as a progressive mayor and strong administrator, as well as a respected and effective spokesman for local government. His service at the Department of Housing and Urban Development will be a contribution to this administration and to the country."

Powell quoted Carter as saying of Goldschmidt:

"Mayor Goldschmidt is known as an aggressive and innovative mayor with outstanding administrative abilities. He understands from personal experience the transportation needs of local governments."

Officials of the U.S. tconference of Mayors, of which Landrieu is a former president, were delighted by the two appointments. The conference's executive director, John Gunther, noted that in one day the number of mayors named to Cabinet positions had doubled.

The other two mayors with Cabinet service were Anthony J. Celebrezze of Cleveland, secretary of health, education and welfare in the Kennedy administration, and Frank Murphy of Detroit, who was appointed attorney general during Franklin D. Roosevelt's second term.

Landrieu, a lawyer, served in the Louisiana House of Representatives and later on the New Orleans City Council during the 1960s. In 1970, he was elected mayor, serving two terms and leaving office in 1978. Since then he has been president of Joseph C. Canizaro Interests, an urban real estate development firm.

Landrieu is a popular figure among the nation's mayors, a politically important group to Carter. He also has ties to such powerful congressional figures as Senate Finance Committee Chairman Russell Long (D-La.).

Goldschmidt, also a lawyer, was elected mayor of Portland in 1972. Before that, he was a lawyer with the Portland Legal Aid Service and a member of the Portland City Council. He is also a former chairman of the U.S. Conference of Mayors' transportation committee and the co-chairman of the National League of Cities' energy task force.

Among the factors that may have figured in Goldschmidt's appointment is that Re. Robert Duncan (D-Ore.), the chairman of the important House Appropriations transportation subcommittee, is from Portland. CAPTION: Picture, President, with aide Jack Watson at left, talks with Neil Goldschmidt, his nominee for transportation secretary. AP