Nola, a senior from Baton Rouge, was chosen in the fifth round by the Miami Marlins. Goody, a junior from Orlando, Fla., was selected in the sixth round by the New York Yankees.
Each player was selected in last season's draft and significantly improved his draft status during the 2012 season. Nola was selected in the 31st round of the 2011 draft by the Toronto Blue Jays, and Goody was selected in the 22nd round last season by the Yankees.
Rounds 2-15 of the MLB Draft were completed on Tuesday. The draft concludes on Wednesday with Rounds 16-40.
Nola, a four-year starter for LSU, is hitting .313 this season with 16 doubles, one triple, four homers and 42 RBI. He was named the Most Outstanding Player last week of the NCAA Baton Rouge Regional.
"It's an honor to be drafted, and it's always been a goal of mine to play pro ball, but my focus right now is on helping LSU get to the College World Series," Nola said. "It's been an incredible experience to have been a part of this program for the past four seasons. It doesn't get any better than LSU Baseball -- this is where my heart is."
Goody, in his first season at LSU after transferring from State College of Florida, has 11 saves, three walks and 45 strikeouts in 33 appearances this season as the Tigers' closer.
LSU signee Hayden Jennings, an outfielder from Evangel High School in Shreveport, La., was selected in the sixth round Tuesday by the Washington Nationals.
LSU first-team all-America pitcher Kevin Gausman was chosen in the first round on Monday by the Baltimore Orioles. Also selected on Monday in Compensatory Round A were LSU signees Joey Gallo (39th selection, Texas Rangers) and Jesmuel Valentin (51st selection, Los Angeles Dodgers).
LSU Draft Summary through Day 2 (draft will conclude Wednesday with Rounds 16-40)
LSU Players selected in the 2012 MLB Draft
Kevin Gausman, RHP, 1st Round, Baltimore, 4th selection
Austin Nola, SS, 5th Round, Miami, 167th selection
Nick Goody, RHP, 6th Round, New York Yankees, 217th selection
LSU Signees selected in the 2012 MLB Draft
Joey Gallo, INF/RHP, Comp. Round A, Texas, 39th selection
Jesmuel Valentin, INF, Comp. Round A, Los Angeles Dodgers, 51st selection
Hayden Jennings, OF, 6th Round, Washington, 204th selection