Sources said Morrow received a $1.5 million contract from St. Louis. He earned $4.1 million last season with the Pittsburgh Penguins.
Morrow, 34, was among many veteran free agents squeezed out this summer by the NHL's lower salary cap.
In St. Louis, he will reunite with familiar faces in coach Ken Hitchcock and general manager Doug Armstrong, both of whom were with Morrow during parts of his 13 seasons with the Dallas Stars.
Morrow, who was part of Canada's 2010 Olympic gold-medal squad, was traded from Dallas to Pittsburgh last season.