Winnik, 30, has four goals and 10 assists in 56 games for the Maple Leafs this season. Capitals general manager Brian MacLellan called him a "versatile player who plays with grit and can be used in all situations."
Laich, 32, has a goal and six assists in 60 games for the Capitals and cleared waivers Sunday. He is in the midst of a 48-game goal drought.
The Capitals will save salary-cap space this season and next with the deal.
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