Also Thursday, pitcher Edinson Volquez (Dominican Republic), outfielder Chris Denorfia (Italy), infielder Jesus Merchan (Spain), pitcher Mark Hardy (Canada) and outfielder Corey Adamson (Australia) were also named to provisional rosters for the Classic, which begins in March.
The MLB Network will broadcast all 39 games of the Classic, Major League Baseball's only international tournament, which will begin with Brazil facing two-time defending champion Japan in Fukuoka, Japan, on March 2, and end with the final game in San Francisco on March 19.
Team USA is in the Arizona bracket with Canada, Mexico and Italy and opens against the Mexicans at Chase Field on March 8. The other three first-round brackets are in Japan; Taichung, Taiwan; and San Juan, Puerto Rico.
Gregerson has a career 2.92 ERA over four seasons in the Major Leagues, all with the Padres. In 2012, he was 2-0 with a 2.39 ERA in 77 games. Gregerson also had a career-best nine saves, filling in for an injured Huston Street as closer at times.
Volquez went 0-1 but didn't allow an earned run in his only start for the Dominican Republic in the 2009 Classic. Denorfia hit .400 in 10 at-bats for Italy in 2009 with three doubles.
Hardy and Adamson are Minor League prospects for the Padres. Hardy, a 24-year-old right-hander from Vancouver, has a career 3.48 ERA over parts of three seasons.
Adamson might be one of the youngest players in the entire Classic. A 20-year-old, Adamson might have played his way onto the Australian team with a hot winter in the Australian Baseball League. Playing for Perth, Adamson was hitting .352 with a .425 on-base percentage in 27 games as of Thursday.
San Diego first baseman Yonder Alonso was asked in December if he had any interest in playing for Spain in the Classic but he declined, citing wanting to stay with the Padres during Spring Training.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter.
This story was not subject to the approval of Major League Baseball or its clubs.