Allen's four-year deal voids down to three years at $24 million, and includes $15.5 million guaranteed, which is in line with the deal DeMarcus Ware signed with Denver.
Allen's deal includes guaranteed base salaries in 2014 and 2015 as well as a fully guaranteed roster bonus due next March.
The deal is strong for both sides.
Allen, a future Hall of Famer at defensive end, had visited Seattle and Dallas previously and came to terms with Chicago "in the wee hours" Tuesday, his agent Ken Harris said. Allen mulled over offers from several teams over the weekend and came to a final decision with his family.
He remains in the NFC North following a long stint in Minnesota and replaces Julius Peppers in Chicago, as Peppers signed in Green Bay following his release by the Bears.
Allen has 11 1/2 sacks last season and is at the top of most pass rushing statistics since entering the league with the Chiefs. Allen was later traded to the Vikings and signed a massive new deal with the Vikings then, which he played out through the 2013 season. This was his first experience with free agency.