The trade is expected to include the Seahawks' 2013 first-round draft choice being sent to the Vikings, sources told ESPN.
It also is contingent on Harvin agreeing to a new contract, which is expected to be finalized in the next 48 hours.
The trade agreement, contingent on Harvin passing a physical, was earlier reported by Fox Sports.
Harvin is scheduled to fly to Seattle on Monday night and will undergo his physical in the next 24 hours, a source said.
The trade cannot be officially completed until Tuesday at 4 p.m. ET, when the 2013 league year officially begins.
Vikings running back Adrian Peterson reacted to the trade through his Twitter account.
"The best all around player I ever seen or you'll ever see! Goes to Seattle! I feel like I just got kicked in the stomach. Several times!!!," he wrote. "I wish my boy Percy nothing but success! God bless you homie."
Seattle has a connection to Harvin. The team's offensive coordinator, Darrell Bevell, held the same job with Minnesota when the Vikings drafted Harvin in 2009. Harvin also will be reunited with receiver Sidney Rice, who was his one-time teammate in Minnesota.
Seahawks cornerback Richard Sherman posted a message on Twitter, welcoming Harvin to the team.
"Welcome to the Team bruh @Percy_Harvin ... Happy to have ya," he wrote.
When asked about the trade, Seahawks receiver Golden Tate, whose spot on the Seahawks' depth chart will be altered with the addition of Harvin, told Josina Anderson that "it's a business."
"The Seahawks are trying to do whatever they think is necessary to put together a Super Bowl quality team. If this is one of the steps they think works to accomplish that, then that's their choice. I don't think it will impact any of our work habits. We are still going to grind and let the cards play out the way that they will," he said.
Last month at the scouting combine, Vikings general manager Rick Spielman insisted he had no intent to deal the receiver, who he called a "dynamic playmaker," and said he wouldn't even take phone calls about a trade.
Harvin, who is entering the final year of his rookie contract, badly sprained his left ankle on Nov. 4 at Seattle last season and didn't play again. The Vikings placed him on season-ending injured reserve a month later.
Harvin made waves last summer when he expressed unhappiness with the organization and requested a trade. By the time training camp arrived, he had simmered down. He went home to Florida for his rehabilitation after he was placed on injured reserve, but coach Leslie Frazier downplayed his absence, noting that others have chosen to do the same.
He started last season playing like a Most Valuable Player award candidate, leading the league in total yards (receiving, rushing and returning) through nine games in 2012 until he was hurt.
Harvin still led the team in receptions (62) and yards receiving (677) despite playing barely half of a season, and he had a kickoff return for a touchdown as well as 96 yards rushing and one score on the ground.
The 24-year-old Harvin has 7,168 all-purpose yards in his four-season career with 29 touchdowns (20 receiving, five return, four rushing). He also has 280 receptions in 54 career games.
Information from ESPN.com senior writer John Clayton, ESPN NFL Insider Adam Schefter, ESPN.com NFC West blogger Mike Sando and The Associated Press was used in this report.