The deals announced Friday are the first the team has reached with this year's draft class.
Veldheer was drafted 69th overall out of Division II Hillsdale College in Michigan. He has played at tackle and center in offseason workouts.
Campbell was picked 106th overall out of Maryland. He has been playing guard since joining the team.
Oakland still has seven other draft picks to sign, including first-rounder Rolando McClain.
The Raiders have also released linebacker and special teams standout Isaiah Ekejiuba.
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