With the roar of airplanes in the background and the flutter of applause in the foreground, federal and local officials publicly congratulated one another yesterday upon the occasion of the long-sought transfer from federal to local control of National and Dulles International airports.

"They said it couldn't be done," Transportation Secretary Elizabeth Hanford Dole said to an audience of 200 people, mostly from federal, state and local transportation departments, who gathered in front of National's main terminal for the ceremony.

Dole spearheaded the Reagan administration's effort to lease the federally owned airports to a regional authority, which plans to issue bonds to finance about $700 million in new terminals, runways, roads, parking areas and other improvements.

The Metropolitan Washington Airports Authority, governed by a board representing Virginia, Maryland and the District of Columbia, officially assumed control of the airports when the lease took effect at 12:01 a.m. Sunday.

"You're off to a flying start," Dole said as she presented the lease to former Virginia governor A. Linwood Holton Jr., who headed the commission that devised Dole's transfer plan and now chairs the authority's board of directors.

Holton, referring to plans that will be applauded by anyone who has sprinted across four lanes of traffic and then walked the three-quarters of a mile from the Metro station to the main terminal, promised that "we're going to put that terminal up next to the subway station where an urban airport terminal ought to be."

Holton said the airport board will "approach the problems of these regional airports with regional considerations in mind," collaborating and cooperating with airlines, passengers, airport neighbors, local governments and a congressional review board created to oversee the authority's major actions.

Virginia was represented at the ceremony by its current governor, two former governors, its transportation secretary and other local officials.

D.C. Mayor Marion Barry was represented by City Administrator Thomas M. Downs, who said the transfer "reaffirms the fact that 'home rule' applies not just to the District, but affects us all in this region."

Barry was feeling "under the weather" yesterday morning after a late night watching fireworks over the Potomac River, said spokesman John C. White. The mayor went to work later in the day to attend meetings, White said.

Maryland Gov. William Donald Schaefer attended Flag Day ceremonies in Annapolis, but intended "no slight on the transfer," said spokeswoman Sue Pimentel. Maryland initially fought the transfer, charging that it would put Baltimore-Washington International Airport at a competitive disadvantage, but dropped its opposition after Dole promised $72 million in federal funds for BWI.

Rep. Norman Y. Mineta (D-Calif.), a member of the congressional review panel and chairman of the House Public Works aviation subcommittee, said that congressional reluctance to pay for improvements at the airports had turned National into "a source of embarrassment" and had transformed Dulles from "an international piece of art" into a place that "now looks like a mobile home park with those temporary midfield facilities."

Mineta said the transfer "created the financial resources that will be used to make badly needed physical improvements at both."