The person spoke on the condition of anonymity Monday night because the club has not yet announced the move.
The 31-year-old Brantley has spent his entire 10-year career with the Cleveland Indians, where he was a three-time All-Star.
Brantley is a career .295 hitter and gives Houston an upgrade to an outfield anchored by centre fielder George Springer.
Brantley hit .309 with 17 homers, 36 doubles and 76 RBIs last season in 143 games, with 134 starts in left field. Brantley’s best season came in 2014 when he finished third in AL MVP voting after hitting 20 homers with 97 RBIs — both career-highs.