Outfielder Kyler Murray, the A’s top pick in last week’s draft, officially will sign with the team Friday and will be introduced at the Coliseum the same day, multiple sources told The Chronicle.

As part of the agreement, Murray will play just one more year of football at Oklahoma, one source said. Murray, who is projected to be Heisman Trophy winner Baker Mayfield’s successor at quarterback, has two years of football eligibility left, but under his deal with Oakland, he will forgo his final season. He will report to the A’s complex in Mesa, Ariz., next spring to begin his full-time baseball career.

Murray, 20, signed for right around the draft-slot value for the ninth overall pick, about $4.6 million.

Both the A’s and Murray have insurance in the event that Murray is severely injured playing football this season.

Progress on injuries: Brett Anderson threw his first bullpen session since going on the disabled list with shoulder soreness May 19, and he said everything felt great. He threw 20 pitches, all fastballs, and he’ll throw all his pitches his next time out, Saturday.

Starter Andrew Triggs threw an extended bullpen session, two sets of 20 pitches with a five-minute break, and all went well, so he’ll throw to hitters in Arizona on Saturday and from there could head on a rehab assignment.

Starter Trevor Cahill remains likely to go on the disabled list Friday with an Achilles tendon problem; he was wearing a walking boot Wednesday. Chris Bassitt would start Friday’s game in his place.

Outfielder Matt Joyce (back) said he hit off a tee for the first time since going on the DL on June 3 and felt no issues.

Minor-league starter James Kaprielian, whose recovery from Tommy John surgery was interrupted by shoulder soreness, has started playing catch again. Another minor-league starter returning from Tommy John surgery, former Cal right-hander Daulton Jefferies, will make his first start since surgery when he takes the mound in the Arizona League next week.

Susan Slusser is a San Francisco Chronicle staff writer.