Martinek, 36, played for Columbus last season, but only made seven appearances due to injury.
He is a draft choice of the Islanders (No. 228 in the 1999 NHL Draft), who played the first 453 games of his career with the team before joining Columbus. He has also appeared in nine stanley cup Playoff games, all with the Islanders.
He has 22 goals and 82 assists for 104 points in his NHL career.
Martinek played in four games with Ceske Budejovice of the Czech league during the lockout.
He is one of nine defenseman on the team's training camp roster.
On Sunday, the team also announced eight call ups to training camp.