Anderson, who had played his entire career for the Angels, agreed to a one-year deal worth approximately $2.5 million, the Atlanta Journal-Constitution reported Sunday.
Anderson is expected to undergo a physical on Monday or Tuesday, a person familiar with the negotiations told The Associated Pres on Sunday on condition of anonymity because the deal hasn't been finalized.
Anderson, 36, is expected to form part of a left-field platoon with Matt Diaz and might bat cleanup against right-handed pitchers.
He hit .293 with 15 home runs and 84 RBIs in 145 games for the Angels last season.
Anderson joins an outfield that produced only 27 homers last season, worst in the majors.
A three-time All-Star, Anderson holds several Angels franchise records, including games played (2,013), runs scored (1,024), hits (2,368), doubles (489), total bases (3,743) and RBIs (1,292). He ranks second in home runs (272) and career batting average (.296).
Anderson helped the Angels win the World Series in 2002, hitting .300 with two homers and 13 RBIs in the postseason. Los Angeles declined to pick up his $14 million option after last season, instead paying a $3 million buyout.
The Braves are counting on Anderson to provide steady play in an outfield full of question marks.
Right fielder Jeff Francoeur, a once-budding star, looked totally lost while batting .239 with 11 homers and 71 RBIs last year. But he hit 29 homers in 2006 and had more than 100 RBIs each of his first two full seasons.
Diaz batted only .244 last season and was limited to 43 games after tearing up his left knee in May.
Information from The Associated Press was used in this report.