Myllys made an early impact on the scouts while playing on the Finnish medal-winning team at the World Junior Championship. At Oslo, Norway, in 1983 he achieved his first international success by leading his team to a silver medal behind the powerhouse Soviets in the under 18 European Junior Championships. He also won twin awards as best goalie and a place on the media's first All-Star team. The following year the silver streak continued in Sweden with the under-20 team again finishing behind the Soviets in the World Junior Championship. This limelight performance made him the Minnesota North Stars' draft pick in 1987 and a year later he joined the club.
Since Minnesota already had a Finnish goalie in Kari Takko, Myllys who also had trouble settling in to the North American style of play spent most of the time in Kalamazoo with the IHL Wings. There he relearned his craft and was twice selected to the IHL All-Star Team. In the NHL, he played with the San Jose Sharks and saw action in 27 games without impressing coach George Kingston, who gave him every opportunity. The Sharks traded his rights to the Maple Leafs, but Jarmo decided to return to Finland.
In the summer of 1994, after two years at home, Lulea HF talked him into moving to Sweden. He has been there ever since, becoming a legend in that country too as the all-time shutout king with 29 zero-goals-against games and counting. He also became the first goalie in the Swedish league to score a goal. His 29 shutouts put him 12 ahead of Ake Liljebjorn, who needed 15 years to achieve his total. Getting a goal was a long-time ambition for Myllys, and on January 16, 1999, his dream came true when, late in a game against Leksand IF, his stickhandling skills were rewarded by an empty-net marker in a game Lulea won 4-2. Myllys claims it was a perfect effort -- the puck sailed through the air and went into the net without anybody touching it.
After his initial season in Sweden, he was offered a contract by the Ottawa Senators but decided to stay put. It turned out to be a good choice. Led by Myllys, Lulea dominated the league. His impressive goals-against average helped the club capture the national title, but it did even better in the playoffs by going all the way to the its first and only gold in national championship play.
Finland has three major achievements in international hockey to date: the first medal ever, which was the Olympic silver at Calgary in 1988; its first world title, which was won in 1995 in Stockholm; and the victory over the best of Canada in the 1998 bronze medal game at the Nagano Olympics. Myllys was part of all three and in 1995 was awarded the trophy as the tournament's best goalie. In addition, he is one of the rare athletes to have won medals in three Olympic tournaments, with a bronze also from the 1994 event in Lillehammer, Norway. In addition to the 1995 gold, he has two silvers from the IIHF World Championships in 1994 at Milan and 1998 at Bern, Switzerland.