The two American Leaguers will join centerfielder Cameron Maybin, who was acquired in an off-season trade with Florida, in the middle defense that last season included David Eckstein at second, Everth Cabrera, Miguel Tejada at shortstop and Tony Gwynn among a platoon of outfielders.
Hudson is a two-time All-Star who has played for National League West rivals Arizona and Los Angeles. He hit .268 in 126 games with Minnesota last season.
The San Diego Union-Tribune said Saturday that Padres signed Hudson for two years and would announce the deal once a physical exam was completed.
Bartlett was the headliner of a six-player trade that included a player to be named later and sends four Padres farmhand, including three pitchers, to Tampa Bay.