Legislation authorizing $20.1 billion for modern air traffic control equipment, airport improvements and other aviation projects won final congressional approval Friday.

The House approved the measure, 410 to 1, a day after the Senate passed it by voice vote. It now goes to the White House for President Reagan's expected signature.

Voting against the measure was Rep. Martin Sabo (D-Minn.), who opposed a provision reducing federal taxes on airline passengers if the money raised is not spent punctually for aviation projects.

The measure orders the Federal Aviation Administration to have at least 15,900 air traffic controllers on the job by Sept. 30.

The FAA has said it has more than 15,400 controllers working. But lawmakers, responding to the growing number of incidents in which planes come dangerously close to one another and complaints about delays at crowded airports, have accused the agency of dragging its feet in hiring more controllers.

The legislation would extend for three years the 8 percent tax on airline passenger tickets and other levies that collect revenues for a special fund the government uses for many aviation projects.

The measure also would extend for 10 more years subsidies paid to airlines forflying to small towns and would order the FAA to require that all airliners within four years carry an instrument that can warn of impending collisions.