NFL Network's James Jones initially reported that Burnett, his former teammate with the Green Bay Packers, will fly to Pittsburgh to finalize the deal. Jones' report was confirmed by his colleague, Ian Rapoport.
Terms of the deal were not disclosed.
Burnett posted 698 tackles, nine interceptions and 7.5 sacks in 102 games over eight seasons with the Packers. He collected 68 tackles and a forced fumble in 12 contests last season.
The 29-year-old Burnett lined up at safety, slot cornerback and linebacker over the last two seasons.
Burnett reportedly is getting the nod over free-agent safety Michael Thomas, who visited the Steelers on Monday. Thomas has served as the Miami Dolphins' special teams captain for the last two seasons.
The Steelers are aiming to fill the void left after the team parted ways with safety Mike Mitchell. The 30-year-old Mitchell recorded 281 tackles, four interceptions and four forced fumbles in four years as a starter.
Mitchell was hampered by injuries in 2017, when he played in 13 regular-season games, including 12 starts. He started the Steelers' postseason game as well.