The long, bitter fight over the Vietnam Veterans Memorial came to an official end yesterday when the National Capital Planning Commission unanimously approved an "entranceway" location for added elements to the memorial in Constitution Gardens.

This proposal to place a 50-foot-high staff flying the American flag and an eight-foot-high bronze statue of three U.S. infantrymen in a copse of trees at the southwest corner of the memorial site was the same as the one approved last month by the Commission of Fine Arts.

Interior Secretary James G. Watt, the third party required by law to approve the placement and design of all elements of the memorial, also has accepted the entranceway concept.

"This, in effect, ends the political controversy over the Vietnam Veterans Memorial," said Robert W. Doubek, project director for the Vietnam Veterans Memorial Fund.

Jan Scruggs, a Vietnam combat veteran as well as founder and president of the VVMF, said that the flag staff could be in place by late spring and the statue by the end of the year, thus completing a saga that began four years ago when he first approached Congress with his idea for a memorial.

The story has been an emotional roller coaster. It began with a widespread show of congressional support for the memorial and a federal donation of the prominent site near the Lincoln Memorial. Then came a design competition that attracted more than 1,400 entries. The result was startling: The competition was won by Maya Ying Lin, a 21-year-old undergraduate at Yale.

A storm of controversy greeted Lin's simple concept of two long walls of polished black granite engraved with the names of Americans killed in that war or still missing in action. Opponents strongly felt the design failed to commemorate the patriotism and sacrifice of America's Vietnam veterans. They forced through a compromise whereby the flag and statue would be added to the memorial.

The battle over the placement of these elements continued for a year. Opponents of Lin's design fought to have sculptor Frederick Hart's realistic statue placed more prominently, in the middle of the field in front of the memorial's walls, with the flag situated behind the intersection of the walls. This option was rejected by the planning commission yesterday. A third option, advanced by the American Institute of Architects, also was rejected.

Though rancor at the outcome still exists in some quarters, no one testified yesterday against the entranceway concept, while many veterans groups again turned out in force to support it.

As did the Commission of Fine Arts last month, the planning commission yesterday reserved the right to rule on several specific issues, including placement of lighting and additional pathways at the memorial and the design of alphabetical directories for the names engraved in chronological order on the walls.

"I don't think you could have had a better ending," commented NCPC chairman Helen Scharf. "The walls are a sad reminder of the waste and sorrow of war. The flag and sculpture are a very successful tribute to the young people who gave service to their country. They end up working together as a statement of healing."