Florida Panthers assistant general manager Randy Sexton announced the deal with the unrestricted free agent on Friday. Terms were not disclosed.
Phoenix is in bankruptcy proceedings and did not plan to re-sign Reinprecht.
The 33-year-old Reinprecht scored 14 goals with 27 assists in 73 games with the Coyotes last season. He has 120 goals and 214 assists in 552 NHL games with Los Angeles, Colorado, Calgary and Phoenix.
The 23-year-old Meyer appeared in four games for the Panthers in 2007-08.