Lee's agent, Harold Lewis, said his client is traveling to Orchard Park to sign the deal Sunday. He didn't disclose terms of the deal. The team declined comment.
Lee, who was released by the Cowboys last week, is expected to compete for the backup job behind Willis McGahee.
Lee played in 14 games last season, running for 128 yards on 27 carries. He sought his release after the Cowboys signed Anthony Thomas.
In March, disgruntled Buffalo running back Travis Henry vowed he wouldn't practice or play for the Bills again. He was disciplined in April after missing the start of a mandatory minicamp.
The four-year veteran has one year left on his contract but has demanded a trade after losing his starting job last season to McGahee. Henry was a starter since his rookie season and was coming off consecutive 1,300-yard rushing campaigns before becoming the backup in October.