Alonso will report to the team's taxi squad.
The Braves signed Alonso as a free agent in February but he never made a regular-season appearance for the team.
Alonso, 32, appeared in 121 games for the Colorado Rockies and Chicago White Sox last year, hitting .199/.296/.346 with 10 homers.
The former All-Star spent four seasons with San Diego from 2012-15. Over those 439 games, the slugger authored a .271/.339/.386 with 27 homers.