Brach, 27, posted a 3.19 ERA with 19 walks and 31 strikeouts in 31 innings over 33 games for the Padres this season. In three major league seasons, Brach has gone 3-6 with a 3.70 ERA in 109 relief appearances, averaging 10.1 strikeouts per nine innings.
In six minor league seasons, Brach registered a 2.34 ERA and recorded 118 saves in 250 relief appearances, posting 10.8 strikeouts and 1.8 walks per nine innings.
The Padres selected Brach in the 42nd round of the 2008 First-Year Player Draft out of Monmouth University in New Jersey.
"He's a strikeout pitcher and he has a good fastball and a good forkball," said executive vice president Dan Duquette. "He's been very competitive. He's had two good years in a row with San Diego and we think he gives us a little bit more depth in the bullpen. He's another option in the sixth and seventh inning."
The Orioles' early offseason activity has centered on the bullpen, including last week's signing of former Rockies reliever Edgmer Escalona.
"We've been focused on adding some pitching depth, and that's been accomplished so far," Duquette said. "We've picked up two pretty good arms here so far."
Brach has a minor league option remaining. He can't become a free agent until 2019.
Duquette said he's still "looking around at other team needs," which include a starting pitcher, left fielder, second baseman and left-handed designated hitter.
"It's only Nov. 25," he said. "We're working to set up the team to be competitive next season."
The Orioles now have 37 players on the 40-man roster. They signed left-handed reliever Kelvin De La Cruz on Nov. 18.
Jones, 23, went 5-7 with a 5.64 ERA in 25 starts for Single-A Frederick (one) and Double-A Bowie (24). The former ninth-round draft pick in 2011 out of Mississippi State went 15-18 with a 4.47 ERA in 67 games, including 34 starts, in three seasons in the Orioles system.
Jones sent the following tweet shortly before the Orioles announced the trade:
"Would like to take this time to thank the @orioles organization for all they have done to help me in my career."
Update: Brach is listed at 6-foot-6, 215 lbs. He won't be difficult to find in the clubhouse next spring.
Brach had some weird splits this season with the Padres. Right-handers batted .365 against him, compared to .232 by left-handers. In three major league seasons, right-handers are batting .245 and left-handers 242.
Brach has a career 2.98 ERA at Petco Park, which favors pitchers, and a 4.56 ERA on the road.