Murphy, Carolina's first-round pick in 2011, spent parts of the past five seasons with the Hurricanes.
They traded him to Calgary along with backup goalie Eddie Lack on Thursday night, but the Flames waived Murphy less than 24 hours later.
Under his deal with the Wild, Murphy will make $700,000 at the NHL level or $350,000 in the minors.
It was part of a busy day for the Wild, who signed six players in all.
Forwards Landon Ferraro and Cal O'Reilly signed two-year contracts Saturday and will be paid $700,000 if they're playing in the NHL and $375,000 if playing in the AHL. Forward Kyle Rau agreed to a one-year contract for $700,000 in the NHL and $200,000 in the AHL. Rau played 24 games last year with the Florida Panthers.
Defensemen Alex Grant signed a one-year contract and will earn $700,000 in the NHL and $300,000 and $350,000 respectively in the AHL.
The Wild signed a one-year, two-way contract with free-agent goaltender Niklas Svedberg, who played 48 games last season with the Salavat Yulaev in the Kontinental Hockey League. The Swede had a .897 save percentage and a 2.99 goals-against average. His record was 14-17-12.