Allen, formerly of the Minnesota Vikings, was named a first team All-Pro four times in his 10-year NFL career and ranks 12th on the league's all-time sack list with 128.5, second only to John Abraham (133.5) among active players.
The deal is worth a total of $32 million, with $15.5 million in guaranteed money going to Allen over the first two seasons, NFL.com reported.
Allen, who turns 32 next month, had 11.5 sacks last season, down from his league-leading peak of 22 in 2011.
Chicago had released their own veteran defensive end, 34-year-old Julius Peppers, who signed a three-year, $30 million free agent contract to join NFC North rival Green Bay Packers earlier this month including $8.5 million for the first year.
The Bears, who allowed their most points and yards ever in a season and tied for last in sacks in 2013, made Allen the fourth defensive end they have signed since the free agency period began on March 11, including Lamarr Houston of the Raiders.
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