Sykora skated with the team on a tryout basis for two practices, and once he passed his physical the deal was done on Thursday.
"I guess I had a good practice," Sykora joked.
The 32-year-old ranked fourth on the Stanley Cup champion Pittsburgh Penguins last season with 46 points in 76 games. He had 25 goals, giving him 300 over his 14-year career. Sykora has played in the Stanley Cup finals five times.
"It's a tough market out there right now," Wild general manager Chuck Fletcher said. "He was surprised he wasn't able to land a job earlier."
Sykora turned down richer offers to play in Russia.
"I'm very excited to be a part of the change here in Minnesota," said the Czech Republic native who has played for five other NHL teams, first with the New Jersey Devils in 1995 after they made him their first-round draft pick.
Under Fletcher and new coach Todd Richards, the plan is to play a faster pace and put more of a premium on offense.
"I guess the team wants to go a different direction and play a little more exciting hockey, and I think I can bring some offense to this team," Sykora said. "I'm excited to be a part of it."
Fletcher was in contact with Sykora's agent, Allan Walsh, over the last six weeks about the possibility of signing him.
"We felt we needed to add one more goal scorer," Fletcher said, referring to the loss of Marian Gaborik this year and Brian Rolston last year. "Petr is a proven scorer. He likes to the shoot the puck and score goals. We feel he'll be a good fit."