Verner, one of the top free agent cornerbacks on the market, reportedly gets $26.5 million over four years and includes $14 million in guaranteed money.
The move all but signals the end cornerback Darrelle Revis' tenure in Tampa Bay. He is expected to be released by 4 p.m. ET on Wednesday.
"I would feel more obliged to go to a team that paid me $6 or $7 million and made me one of the highest-paid players on the team than go to a team that paid me $8 or $9 million and I wasn't one of the highest-paid players on the team," Verner told CBSsports.com.
The 25-year-old Verner led the Titans with five interceptions last season and was fifth on the team in tackles while making the Pro Bowl.
The Verner signing is the third of the day for Tampa Bay, which also added pass rushers Michael Johnson and Clinton McDonald via free agency.