The New York Post first reported the deal, citing sources.
Olsen, 35, signed a one-year, $7 million deal with Seattle in February after being released by the Carolina Panthers in January. The three-time Pro Bowl selection plans to honor that deal and has no set plan on when he will retire, a league source told ESPN.com.
The Fox contract currently plans to pair Olsen with Kevin Burkhardt when Olsen is finished playing. Should the Seahawks not make the playoffs and Olsen opts to retire after this season, he potentially could be moved into an analyst role for the playoffs.
Olsen was considering the move to Fox after his release from Carolina, where from 2014-16 he became the first tight end in NFL history to have three straight 1,000-yard receiving seasons. The Seattle deal and desire to make another run at the Super Bowl he fell short of winning in 2015 at Carolina prompted him to continue playing.
Olsen has made it no secret he would like to pursue a career in sports broadcasting once his football career is over. He received rave reviews for his appearance as a guest analyst for Fox Sports during Carolina's bye week the past two years.
He also has appeared on ESPN's Postseason Super Bowl Countdown Show the past two years.
But Olsen also has been clear he still can be among the NFL's top tight ends, that only a foot injury in 2017 and '18 slowed him down. He caught 52 passes for 597 yards this past season at Carolina.
The Panthers opted to move on from Olsen and a 2020 $11,675,000 salary-cap number as they begin to rebuild under new coach Matt Rhule.
"The team and I are both on the same page that it is best we go in different directions for now," Olsen said in a statement released by the team after his release. "On the field, I will always cherish the nine seasons we shared together. The wins, the losses, standing at midfield holding the Halas Trophy as NFC champs. The reality of going to the Super Bowl was beyond words, as was the disappointment of falling short.''