The assigned value of the ninth pick is $4,761,500.
Murray, who backed up Heisman winner Baker Mayfield last season, was projected to succeed him at Oklahoma. Now he'll have a difficult decision to make about his football and baseball careers.
"Right now I'm not focused on the baseball-football situation," Murray told reporters Monday night in a conference call, while adding that he planned to play football in 2018.
Murray could sign with Oakland and still play at least this season for the Sooners. Or, he could spurn football and move forward with the A's and baseball. Murray would still have his football scholarship, provided he still met his 12-hour academic requirement, even if he signed a pro baseball contract.
"The risk of the football was, in our opinion, outweighed by the upside on the baseball field," A's scouting director Eric Kubota said. "We were totally on board with his desire to play quarterback at Oklahoma. Frankly, we're kind of excited to be Oklahoma fans for 12 games."
Last week, Oklahoma coach Lincoln Riley said he expected Murray to be with the Sooners this season regardless of what happened in the MLB draft.
"I knew the deal when we were getting into it. [The Murray family has] lived up to their word in every part of it," said Riley, who added that Murray would not be playing summer baseball and instead would work out with the football team.
Riley reiterated that point Tuesday.
Statement from head coach Lincoln Riley on Kyler Murray: pic.twitter.com/j4Mhl1qgWP— Oklahoma Football (@OU_Football) June 5, 2018
Murray, a former five-star recruit in football, has been coy about splitting baseball and football going forward, saying he was "not worried" about the draft.
Murray hit cleanup and played center field this season for the Oklahoma baseball team, which was eliminated in regional play Monday by Mississippi State. He hit. 296 with 10 home runs, 47 RBIs and 10 stolen bases.
In limited time behind Mayfield last year, Murray completed 18 of 21 passes for 359 yards. He also rushed for 87 yards and three touchdowns.
Murray transferred to Oklahoma following the 2015 season after originally signing with Texas A&M.
Murray isn't the only football player who has a decision to make with this MLB draft, though. Jordyn Adams was selected No. 17 overall by the Los Angeles Angels on Monday and will have to choose between major league baseball or honoring his national letter of intent to North Carolina.
Adams was the No. 163-ranked prospect in the 2018 recruiting class for football and signed with the Tar Heels to play football and baseball. At 6-foot-1, 180 pounds out of Morrisville, North Carolina, Adams was the No. 24 wide receiver in his class. He excels at football and baseball, but also had a video go viral that showed Adams dunking over a classmate. Adams was the No. 19 prospect in Keith Law's Top 100 prospects before the draft.
ESPN's Tom VanHaaren contributed to this report.