Kaprizov won't be eligible to participate in the upcoming postseason.
The 23-year-old spent the last six seasons playing in the KHL after the Wild selected him in the fifth round of the 2015 NHL Draft. He amassed 33 goals and 62 points with CSKA Moscow this season.
"We are thrilled to officially sign and welcome Kirill to our organization," Wild general manager Bill Guerin said. "He has exceeded all expectations in his development since he was drafted in 2015. Kirill is a smart and dynamic forward that has led the KHL in goals each of the past two seasons and we look forward to having him on our roster when next season starts."
Kaprizov was a five-time KHL All-Star and helped lead CSKA Moscow to a Gagarin Cup victory in 2018-19. He led the league in scoring for the past two seasons and also became the youngest player in KHL history to hit the 100-goal mark.