President Carter told the American Public Transit Association here today that he had appointed former Washington Metro general manager Theodore C. Lutz to head the Federal Urban Mass Transportation Administration.

Lutz's appointment, which is subject to Senate confirmation, had been sought by new Transportation Secretary Neil Goldschmidt, who was himself confirmed only last Friday.

The appointment announcement was an addition to Carter's prepared text in his speech to 3,000 state and local transit officials attending a convention at the New York Hilton. It was greeted with sustained applause.

"Ted Lutz," Carter said, "is one of you."

"It is a first-rate appointment," said Alan Kiepper, general manager of the Metropolitan Atlanta Rapid Transit Authority. "Ted can land on his feet and know what he is doing right away, and we can talk to him."

Lutz, who was deputy undersecretary in the Department of Transportation during the Nixon and Ford administrations, served as Metro general manager from November 1976 to April 1979, when he resigned, stating he was "burned out."

Four months later, however, with Goldschmidt in office, Lutz said he would take the UMTA job if it were offered. He said today that the first time he knew for certain he would get the job was "when they called this morning and asked me to expedite my FBI forms."