The 28-year-old Hardy hit .268 with six home runs and 38 RBIs last season. He was an All-Star in 2007 with Milwaukee when he hit .277 with 26 homers and 80 RBIs.
"We're looking for a little more offense to our regular shortstop position, and we're confident he can provide that," Orioles president of baseball operations Andy MacPhail said. "We also talked to other shortstop targets."
Cesar Izturis was Baltimore's starting shortstop last season. He hit .230 with one homer and 28 RBIs and since has become a free agent.
The trade was the Orioles' second of the winter meetings aimed at getting more production from the left side of the infield. They got strikeout-prone slugger Mark Reynolds from Arizona for two relievers.
Hardy played in just 101 games in his lone year with the Twins while dealing with several injuries.
The 30-year-old Harris hit .157 in a limited role. The utilityman fell out of favor with the Twins and spent much of last season in the minor leagues.
Hoey and Jacobson are two hard-throwing minor leaguers who could eventually help replenish Minnesota's bullpen.
The 27-year-old Hoey was 4-0 with a 3.38 ERA and 32 strikeouts in 21 1/3 innings at Triple-A Norfolk. He pitched for Baltimore in 2006-07, going 3-5 with an 8.13 ERA.
The 24-year-old Jacobson was 8-1 with one save and a 2.79 ERA and 67 strikeouts in 71 innings at Class A Frederick. The Orioles got him in August 2009 from Detroit in a trade for Aubrey Huff.
The Orioles also reached a preliminary agreement with pitcher Koji Uehara on a one-year contract for $3 million. The deal is pending a physical.
The 35-year-old Japanese righty was 1-2 with 13 saves and a 2.86 ERA in 43 games for Baltimore last season.