The Seahawks made the roster moves on Thursday, two weeks before the start of training camp.
Martin was a long shot to make Seattle's roster, despite playing in four games for the Seahawks last season. Martin had four catches for 42 yards in his one season with the Seahawks. He previously spent time with Carolina and Jacksonville.
Nelson snapped in six games last season for San Diego before being released by the Chargers in May. He signed with San Francisco but was released by the 49ers earlier this week.