The Raiders previously took linebacker Khalil Mack with their first-round pick Thursday. Oakland still has the third pick in the third round, 67th overall, to make Friday.
Patriots quarterback Tom Brady will be 37 in August and doesn't appear near retirement, but Garoppolo, who says Brady is his favorite player, provides insurance at the position.
Ryan Mallett is the current New England backup, but there have been reports he is on the trading block. Mallett has one year remaining on his rookie contract.
The 6-foot-3, 222-pound Garoppolo threw for 5,050 yards and 53 touchdowns with nine interceptions in 2013. He also ran for four touchdowns and was the winner of the Walter Payton Award, which goes to the top player in FCS.
Information from ESPN Raiders reporter Paul Gutierrez and The Associated Press was used in this report.