Fluker's deal is for one year, according to the source.
It's not clear where the 27-year-old Fluker will fit along Seattle's offensive line. He played right guard for the past three seasons after beginning his career at tackle. Ethan Pocic finished his rookie season in 2017 as Seattle's starting right guard but has also played left guard and right tackle. Luke Joeckel, Seattle's starter at left guard for much of last season, is an unrestricted free agent.
The agreement was first reported by the NFL Network and CBSSports.com. The financial terms of the deal weren't immediately available.
Fluker spent last season with the New York Giants, appearing in nine games with six starts, after beginning his career with the Chargers, who drafted him 11th overall out of Alabama in 2013. In Seattle, he'll reunite with offensive line coach Mike Solari, who was hired by the Seahawks this offseason after spending the past two seasons in the same capacity with the Giants.
The Giants signed Fluker on the cheap last offseason to a one-year, $3 million deal. He began the 2017 season on the bench before working his way into the Week 4 starting lineup at right guard, where he was a difference-maker in the run game when healthy.
New York averaged 110.5 rushing yards per game in games started by Fluker. Without him in the lineup, the Giants averaged just 86.1 rushing yards. He tried to play through foot and knee injuries, but he was placed on injured reserve on Nov. 27, ending his season.
Fluker became a free agent last offseason after the Chargers declined the fifth-year option on his rookie contract. After beginning his career at tackle, Fluker shifted inside to guard in 2015. He appeared in 59 games -- all starts -- in his four seasons with the Chargers.
ESPN's Jordan Raanan contributed to this report.