Edmunds, 24, can earn $72 million over four years with $50 million guaranteed at signing, ESPN reported.
Davis' deal is worth up to $30 million with $19.25 million guaranteed over three years.
NFL Network and ESPN reported the deal for Edwards includes $12.5 million in total guarantees and is worth a total of $19.5 million. Bears assistant general manager Ian Cunningham helped bring Edwards to the Philadelphia Eagles as an undrafted free agent in 2020.
Free agent contracts with new teams are not official until the new league year begins on Wednesday.
Edmunds had five 100-tackle seasons with the Buffalo Bills, who drafted him 16th overall in the 2018 draft.