Burrows signed a minor-league contract with Atlanta on Feb. 23 and assigned him to Double-A Mississippi.
Burrows elected free agency Oct. 21 after the Dodgers outrighted him off the 40-man roster.
The Dodgers selected Burrows' contract from Triple-A Oklahoma City on Thursday.
The Dodgers sent Burrows to minor league camp, according to Juan Toribio of MLB.com.
Burrows announced Tuesday via his personal Twitter account that he agreed to a minor-league contract with the Dodgers.
Burrows accepted an outright assignment to Triple-A St. Paul on Thursday, Brandon Warne of Access Twins reports.
Burrows was optioned to Triple-A St. Paul on Tuesday.
Burrows (0-1) was the pitcher of record in Monday's 11-1 loss to the White Sox after surrendering seven runs (six earned) on five hits and three walks across two innings.
Burrows will serve as an opener in Monday's game against the White Sox, Do-Hyoung Park of MLB.com reports.
The Twins recalled Burrows from Triple-A St. Paul on Tuesday, Aaron Gleeman of The Athletic reports.