Samardzija likely will be placed in the White Sox's rotation behind staff ace Chris Sale and in front of Jose Quintana.
The White Sox will send infielder Marcus Semien, right-hander Chris Bassitt and a third player to the A's, the San Francisco Chronicle reported.
Robertson agreed to a four-year deal with the White Sox that is worth $46 million, a source confirmed to ESPN.com's Jerry Crasnick. The club's bullpen was among the worst in baseball last season, plagued by injuries and struggles.
Samardzija moved into the Chicago Cubs' rotation in 2012 and has gone 26-42 as a starter with a 3.86 ERA. He went a combined 7-13 last season with a 2.99 ERA with both the Cubs and A's. He was 5-6 in 16 starts in the American League, posting a 3.14 ERA.
He is expected to make between $9 million and $10 million in 2015, his final year of arbitration eligibility. The former Notre Dame wide receiver will hit free agency after the 2015 season.
White Sox outfielder Adam Eaton took to Twitter to express his excitement over the team's acquisitions.
Roberston went 4-5 with 39 saves and a 3.08 ERA after taking over the closer role in New York last year from Mariano Rivera. The 29-year old has a 2.81 ERA over seven seasons. Robertson will take over at closer for a White Sox team that hasn't been set in that spot since Addison Reed was traded to the Arizona Diamondbacks last offseason.
The right-hander was an All-Star in 2011 and won a World Series with New York in 2009. He was paid $5,215,000 million in 2014. The Yankees made a one-year qualifying offer of $15.3 million to Robertson for 2015, ensuring them draft-pick compensation if he signs with another team.
Because the White Sox had among the top 10 initial picks in next year's amateur draft, they lose a second-round selection next June rather than their first-round choice, which is eighth overall. The Yankees receive an extra pick between the first and second rounds.
The White Sox had a 4.28 ERA from their bullpen this past season, 28th in baseball and better than only the Colorado Rockies and the Houston Astros. The club's combined 36 saves were better than just five other major league teams.
Information from The Associated Press was used in this report.
White Sox Make Major Moves
Buster Olney discusses how the Chicago White Sox's trade for Jeff Samardzija and the signing of closer David Roberston will impact the team's pitching staff.
White Sox Add Arms
The "Baseball Tonight" crew broke down the impact right-hander Jeff Samardzija and closer David Robertson will have on the White Sox.