Arcia, 26, has spent all six of his major league seasons with Milwaukee. He had one hit in 11 at-bats this season, and he had a .260 batting average in 2020 with 5 home runs and 20 RBI.
He has mostly played as a shortstop but has also seen time at third base and in the outfield.
Overall, Arcia has a career .244 batting average with 42 home runs, 180 RBI and 39 stolen bases. He had signed a one-year, $2 million deal with the Brewers in December.
"He's kind of an up-and-coming guy,'' Braves manager Brian Snitker said. "I was a little surprised he was available. Any time you can upgrade and add to depth at the shortstop position it's really a good move.''
This move clears the way for Luis Urias to take over as the Brewers' everyday shortstop. The Brewers had acquired the 23-year-old Urias along with pitcher Eric Lauer from San Diego in a November 2019 trade that sent outfielder Trent Grisham and pitcher Zach Davies to the Padres.
"The trade is a commitment to Luis Urias,'' Brewers manager Craig Counsell said. "That is a commitment that we made. He has earned this and it's an important time for him. He's going to get a great opportunity here.''
Sobotka, 27, had a 5.36 ERA and 61 strikeouts in 50 relief appearances for the Braves over three seasons. Weigel, 26, gave up 2 runs in 2/3 of an inning in his only major league relief appearances with Atlanta last season.
Sobotka and Weigel will report to the Brewers' alternate training site in Appleton, Wisconsin.
"We think this is a deal that made sense for both sides,'' Brewers president of baseball operations David Stearns said. "We do think that continuing to ensure that we have the pitching needed to make it through this season is important. These are two guys with big, power arms _ very big people in general -- and we think they'll be able to help us through the course of the season.''
The Associated Press contributed to this report.