Wellman has appeared in 41 NHL games, all with the Minnesota Wild, with four goals and nine assists. He was traded to the Rangers in February and spent this past season in the American Hockey League.
The 24-year-old Wellman played his college hockey at Massachusetts.
Florida general manager Dale Tallon calls Wellman "a young, highly skilled forward" who may have the chance to play both center and right wing with the Panthers.
Florida opens training camp in mid-September.