They also signed veteran free agent defenseman Igor Kravchuk.
Bure appeared in the 2000 All-Star Game, but has struggled since. Limited to 31 games last season by a pair of knee surgeries, he totaled just eight goals and 10 assists.
This season, the 28-year-old Russian again has been bothered by knee injuries and has five goals and 21 assists in 46 contests.
Van Ryn, 23, was a 1998 first-round draft pick of the New Jersey Devils who left college to play major junior hockey and later signed with the Blues. He had three assists in 20 games with St. Louis, but spent most of this season in the American Hockey League with Worcester, totaling two goals and nine assists in 33 games.
"He is a first-round draft pick and a great skater with a huge upside," said Panthers General Manager Rick Dudley. "He is another young defenseman with an inordinate amount of talent. Giving up Valeri was tough because he is such a good man. I personally like him a lot, but this was ultimately in the best interest of the hockey club."
St. Louis also obtained a conditional 2004 draft pick.
Kravchuk, 36, has not played this season after collecting four goals and 22 assists in 78 games with the Calgary Flames in 2001-02. The 11-year NHL veteran also represented Russia at the Salt Lake City Olympics.
"We're not worried about Igor being in shape," Dudley said. "Igor is always in shape. Igor is a veteran defenseman with both leadership qualities and a great deal of skill."
In Florida, Kravchuk will be reunited with Mike Keenan, who coached him for parts of two seasons with St. Louis.