Laviolette's deal is for three years, according to TSN's Darren Dreger.
He'll replace Todd Reirden, who was recently fired after two years as head coach. The Capitals found success during the regular season but failed to advance past the first round of the playoffs in both years under Reirden.
The Nashville Predators fired Laviolette in January during his sixth season with the club, which he led to the 2017 Stanley Cup Final.
Laviolette has also had coaching stints with the Philadelphia Flyers, Carolina Hurricanes, and New York Islanders. He won the Cup with Carolina in 2006 and is one of only four coaches in NHL history to lead three different teams to the Stanley Cup Final.