Ponikarovsky had 14 goals and 19 assists with New Jersey and Carolina last season.
The 32-year-old has 135 goals and 179 assists in 636 career games with Toronto, Pittsburgh, Los Angeles, Carolina and New Jersey since being drafted 87th overall in 1998 by the Maple Leafs.
Meech, 28, signed a two-way deal after an injury shortened season.
He returned for the St. John's IceCaps' AHL playoff run, contributing four goals and five assists in 15 games.
Meech has four goals and 12 assists in 128 NHL games with Detroit and Winnipeg.
The five-foot-11, 196-pound blue-liner was drafted by the Red Wings 229th overall in 2002.