LaRoche, Burnett become free agents
LaRoche bypassed a $10 million option for 2013, while Burnett would have earned $3.5 million next season under his old deal.
The Nationals still could sign both players, who can have a chance to test the free-agent market.
LaRoche's 33 homers and 100 RBIs helped the Nationals win their first NL East division title this season, and he collected his first Gold Glove this week.
Burnett went 1-2 with a 2.38 ERA and 57 strikeouts in 56 2-3 innings over 70 appearances in 2012.