The deal is for one year, the source said, meaning Benjamin will be a free agent this offseason.
The Chiefs, who recently released one of their top offensive threats in running back Kareem Hunt and have another, wide receiver Sammy Watkins, limited by a sore foot, are hopeful that Benjamin can help fill the void.
Benjamin, 27, was released by the Bills earlier this week and cleared waivers Wednesday. He caught 23 passes for 354 yards and a touchdown in 12 games for the Bills this season.
Benjamin's best season came in 2014 for the Carolina Panthers, who drafted him that year in the first round. Benjamin caught 73 passes with nine touchdowns as a rookie.
Benjamin missed all of 2015 with a torn ACL and hasn't been the same player since. His production has decreased each season, and the Panthers last year traded him to the Bills.
The Chiefs released Hunt last week after video surfaced of him shoving and kicking a woman. Watkins has missed two of the past three games because of a sore foot. Watkins has practiced both days this week on a limited basis.
The Chiefs have used Chris Conley and Demarcus Robinson in Watkins' absence. Benjamin could challenge them for playing time later in the season, particularly if Watkins' absence continues.