Brady is 40 years old, while Harrison is 39 and turns 40 on May 4.
Harrison visited the Patriots on Tuesday after clearing waviers and becoming a free agent following his release by Pittsburgh. According to a report from CBS Sports over the weekend, the Patriots and Baltimore Ravens are both interested in adding the veteran to their mix.
Before the deal was finalised, Harrison was mulling other options around the league, including a return to the Steelers.
The Patriots have been thin at defensive end and outside linebacker all season.
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"We make the decisions that we feel give us the very best chance to win". He's appeared in 19 postseason games in his career - including victories in Super Bowls XL and XLIII - and has 11 sacks in those games. Harrison briefly retired in September 2014 following a forgettable 2013 season in Cincinnati but returned when the Steelers ran into injury trouble. But that matchup with Fisher had to be fresh in their minds.
The New England Patriots have won their fourth Super Bowl in the Brady/Belichick Era by defeating the Seattle Seahawks 28-24 in Super Bowl XLIX in Arizona.
The Steelers and Patriots each secured a bye through to the divisional round, though New England can clinch home-field advantage throughout the AFC playoffs with a win over the Jets in its regular season finale Sunday. The Patriots know they can't let him sit back all day and throw deep again if that meeting occurs again.