Harrison cleared waivers on Monday to become a free agent. The Steelers released Harrison, the franchise's all-time sacks leader, on Saturday to make room for right tackle Marcus Gilbert, who is returning from suspension.
The Patriots have been thin at defensive end/outside linebacker for most of the season. They have Trey Flowers atop the depth chart at their end-of-the-line position, with rookie Deatrich Wise and Eric Lee behind him. The team also uses linebackers Kyle Van Noy, Trevor Reilly and Marquis Flowers at the end of the line, depending on the package.
Harrison, 39, has 80 1/2 sacks in a Pittsburgh uniform, including at least five sacks in each of the past three regular seasons despite playing a part-time role. Harrison also came up big in the Steelers' past two playoff runs with multiple sacks.
Harrison has played 40 snaps through 14 games this season, compared to 587 last year. He signed a two-year deal in March.
ESPN's Mike Reiss and Jeremy Fowler contributed to this report.