The signing, which cannot be official until the start of the new league year at 4 p.m. ET Wednesday, comes in the wake of longtime Steelers tight end Heath Miller's retirement in February.
The Steelers are high on Jesse James, last year's fifth-round pick, but a Green signing adds depth and playmaking. Plus the Steelers value tight ends who block, and they feel Green is an adequate blocker.
Green played well while Antonio Gates sat out the first part of the 2015 season for a suspension, totaling 14 receptions for 174 yards and two touchdowns through the first four games.
The 2012 fourth-round pick did not have much of an impact in the second half of the year, as nagging injuries slowed his production. In his final eight games, Green totaled 11 catches for 125 yards and zero touchdowns. He finished the season on injured reserve with an ankle issue.
Gates re-signed with the Chargers on Wednesday, agreeing to a two-year contract.
For the 2015 season, Green played 627 offensive snaps, totaling 37 catches for 429 yards and four touchdowns. Green averages 14.1 yards per reception for his career and turns 26 years old in May.
ESPN's Jeremy Fowler and Eric D. Williams contributed to this report.