The White Sox, who reached a one-year deal with Dayan Viciedo on Monday, have no other arbitration-eligible players remaining.
Beckham, who just closed out his fifth season with the White Sox, will earn $4.175 million in 2014. He has one more year of arbitration remaining before becoming eligible for free agency in 2016.
The 27-year-old former first-round draft pick missed a third of the season with a broken bone in his right hand. He ended up playing in 103 games, batting .267 with 22 doubles, five home runs and 24 RBIs. In 142 at-bats in the No. 2 spot of the order, he batted .190 with a .245 on-base percentage, while collecting 154 at-bats in the No. 8 spot, batting .325 with a .375 OBP.
Beckham, a former shortstop at the University of Georgia, owns the second- and third-highest fielding percentages for a White Sox second baseman in a single season. His .9899 mark in 2012 and his .9889 number in 2011 trail only Nellie Fox's .9901 fielding percentage in 1962.
De Aza, who has spent the past four seasons in the White Sox organization, will earn $4.25 million in the upcoming season. He is also eligible for free agency in 2016.
Hitting primarily leadoff, De Aza posted career bests in home runs (17) and RBIs (62). The focus toward more power came with a price, though, as De Aza's batting average and on-base percentage both fell in 2013, while his strikeout total went from 109 in 2012 to 147 last season. On top of that, the center fielder struggled both defensively and on the base paths.
After two seasons as the starting center fielder, De Aza is expected to be the White Sox's fourth outfielder in 2014 after the team acquired Adam Eaton from the Arizona Diamondbacks last month. As the roster stands now, De Aza would be the highest paid outfielder on the team.