Earlier on Tuesday, ESPN's Adam Schefter reported that Tate was visiting the team and expected to sign.
Tate, 26, played for the Browns and Vikings during the regular season, finishing with 371 rushing yards and four touchdowns. He was released by the Vikings last week and has been added to Pittsburgh's 53-man active roster.
Steelers starting running back Le'Veon Bell hyperextended his right knee in the regular season finale, but an MRI revealed there was no structural damage. Coach Mike Tomlin said the team will decide on Bell's status for Saturday's game against the Ravens later in the week.
Bell led the Steelers with 1,361 rushing yards and eight touchdowns this season while also catching 83 balls for 854 yards and four touchdowns.
The Steelers released running back LeGarrette Blount earlier this season after he left a game early after not getting any carries. After the Steelers cut him, Blount signed with the New England Patriots.
Pittsburgh finished 11-5 and won the AFC North. It plays host to the Baltimore Ravens on Saturday at 8:15 p.m. ET.
- Paul Palladino