The 1288 hectare area is within the boundaries of, but not part of, Kakadu National Park.
It was excluded from the park because of its potential to be the site of a uranium mine, as recommended in 1977 by the Ranger Uranium Mine inquiry.
Mr Burke said that over the years a number of mining lease applications had been made, but none granted.
The final legal step, the repeal of the 1981 law, was necessary to prevent mining and preserve Koongarra's treasures for ever.
Mr Burke, after completing his formal speech introducing the repeal bill, added an emotional tribute to Mr Hawke and Mr Lee.
He said during his government, Mr Hawke - against the advice of almost all his cabinet - made a judgment call to expand the park which history had shown was absolutely right.
He put his authority on the line to protect "one of the most precious places on earth".
Mr Burke said Koongarra remained "a hole in the heart" of Kakadu.
Mr Lee, the last of the Djok clan traditional owners, had been offered millions of dollars to allow mining.
But he wanted to leave his land in as good a state as his ancestors had.
He'd also gone to Paris in 2011 to tell the World Heritage Committee why his land should be added to Kakadu.