The Jets traded a second-round pick in both 2022 and 2023 for the defenseman, who is entering his 11th NHL season and has 654 career games played.
Dillon, 30, had 19 points in 56 games for the Capitals last season. He was acquired from the San Jose Sharks in February 2020 and signed a four-year, $15.6 million contract with Washington in October.
A defense-first defenseman, Dillon primarily played with John Carlson, the Capitals' top defenseman, last season.
The trade allows Winnipeg to bolster the weakest facet of its lineup while allowing Washington to pare down its roster of defenseman.
Prior to the trade, the Capitals had roughly one third of their salary-cap space dedicated to the blue line. Washington now has just over $13.6 million in cap space available.
It's anticipated the Capitals will announce a new contract for free-agent star Alex Ovechkin at some point this week.
The trade leaves Washington with six veteran defenseman under contract for next season. Zdeno Chara, the 44-year-old great who played for the Capitals last season, is an unrestricted free agent and has yet to decide whether he'll return to play in the NHL.
The Jets also re-signed veteran forward and former NHL All-Star Paul Stastny on Monday, the team announced. Stastny, 35, secured a one-year deal worth $3.5 million to stay in Winnipeg after a season in which the Jets advanced to the second round of the Stanley Cup playoffs.
Stastny had 13 goals and 29 points last season, appearing in 56 regular-season games. He had one goal in the postseason, during which the Jets defeated the Edmonton Oilers before bowing out versus the Montreal Canadiens.
The son of Hockey Hall of Fame forward Peter Stastny, Paul Stastny was selected by the Colorado Avalanche in the second round of the 2005 NHL draft. He has played 1,001 career regular-season games, amassing 755 points.