The move also gives the Islanders some cap room as Zhitnik has two years and US$7 million left on his contract while Meyer will earn just $525,000 this season and next.
Zhitnik joined the Islanders last year after playing 10 seasons in Buffalo. He has two goals and 11 points in 30 games this year.
Meyer signed with the Flyers in 2003 after going undrafted. In 83 NHL games over the past three years, he has eight goals and 32 points - including two goals and five points in 25 games this season.