The Chargers have a third draft choice agreed to terms. They have three to go.
Ian Rapoport of NFL Media reports the deal is worth $13 million.
Murray was a three-year starter at Oklahoma. He earned second-team All-America honors last season.
The Chargers traded up with the Patriots to draft Murray with the 23rd overall choice.
He made 325 tackles, 9.5 sacks, a forced fumbled and six pass breakups in his 40 games over three seasons.