The people spoke to The Associated Press on condition of anonymity Saturday because the Orioles have not announced the transaction.
The 29-year-old Davis has been with Baltimore since 2011. He hit a major-league leading 47 home runs and amassed 117 RBIs last year.
Davis became a free agent after the 2015 season. The Orioles were his most aggressive suitor, offering a seven-year deal last month.
Davis stalled making a decision. His decision to agree to terms came days after Baltimore reportedly made an offer to hard-hitting free agent Yoenis Cespedes.
Davis has 203 career homers, including 126 over the last three years. He hit a career-high 53 long balls in 2013.