The team announced the deal with the restricted free agent on Tuesday.
Burakovsky, 22, had 12 goals and 23 assists in 64 games for Washington last season, his third in the NHL.
He has 38 goals and 57 assists in 196 games with the Capitals, who drafted him in the first round in 2013.
The Capitals were the Presidents' Trophy winners for the second time in a row last season, but they lost to the Pittsburgh Penguins in the second round of the playoffs.
They re-signed center Evgeny Kuznetsov to an eight-year, $62.4 million deal and kept right winger T.J. Oshie and defenseman Dmitry Orlov. Washington still has not re-signed backup goaltender Philipp Grubauer.