Streit, the Islanders' team captain, had six goals and 21 assists in 48 games this season, and added three goals and two assists in six playoff games. The deal was announced Wednesday.
The 35-year-old Streit joined the Islanders as a free agent in 2008, led the team in scoring his first season with 56 points and was an All-Star.
He bolsters Philadelphia's blue line, which was decimated by injuries last season.
Harper had 20 goals and 21 assists over parts of four seasons with the AHL's Phantoms.