"I'm going to Philly," he told ESPN.
The Eagles had to fend off the Seahawks, who made a last-ditch effort to bring Maxwell back to Seattle rather than have him go to Philadelphia, sources told ESPN.
When the deal is completed Tuesday, it is expected to pay Maxwell $63 million over 6 years, with $25 million guaranteed, sources told ESPN.
Philadelphia released starting cornerback Cary Williams last week and Bradley Fletcher, the team's other starting cornerback last season, is scheduled to be an unrestricted free agent.
Maxwell, 27, was a sixth-round draft choice out of Clemson by the Seattle Seahawks in 2011.
He took over as a starter in the final five games of the 2013 season and had four interceptions, playing so well that the Seahawks didn't make an effort to re-sign starting cornerback Brandon Browner or backup Walter Thurmond.
Except for three games when he was out with an injury, Maxwell was a starter all season in 2014. With quarterbacks trying to avoid throwing at cornerback Richard Sherman, Maxwell was tested often (once every 5.7 snaps) but without much success from opposing quarterbacks, who averaged only an 81.1 passer rating against him.
Maxwell had two interceptions and 12 passed defensed in 2014. He played both the outside corner spot and the nickelback spot at different times last season.
ESPN.com Seahawks reporter Terry Blount contributed to this report.