Jenkins was selected No. 41 overall by the Redskins, and ahead of former Tiger defensive end Da'Quan Bowers.
Jenkins was a first team All-ACC defensive tackle last year when he had 53 tackles, including nine tackles for loss.
Gilchrist was selected by San Diego with the No. 50 selection.
The North Carolina native had 66 tackles to rank fourth on the team in 2010 and he also led the Tigers in punt returns and kickoff returns.
Da'Quan Bowers, originally thought of as a first round lock, was drafted after Gilchrist with the No. 51 overall pick (Tampa Bay).
Bowers led the nation in sacks with 15.5 and was second in tackles for loss with 26 in 2010.
He was also the recipient of the Bronko Nagurski Award as the National Defensive Player of the Year by the Football Writers Association, and winner of the Ted Hendricks Award as the top defensive end in college football.
The Bucs also drafted former Clemson defensive end the late Gaines Adams four years ago with the No. 4 overall pick.
As many as two other former Tigers could be selected either in the second or third round of tonight's draft.
Jenkins, Gilchrist, Bowers drafted
CUTigers.com Top Stories
Pagano to TransferAfter helping Clemson win a National Championship and earning his degree, Scott Pagano has decided it is time for him to move on.
CUTigers.comFriday at 11:58 AM
RECRUITING RADARIn our weekly Recruiting Radar, CUTigers Recruiting Analyst Gary McDaniel updates you on the latest news and intel on the Clemson recruiting front!
TIGERS TAKE A W FROM WAKEAfter back-to-back heartbreaking losses to Syracuse and Duke, the Tigers built a 21-point lead on Wake Forest and won by 12 to complete the season sweep of the Deacs and keep their…
DEJA BLUEFor the second straight game, Clemson had the lead or a chance to win on the final possession of the game and came up just short. This time, it was against #18 Duke in the most…
NATIONAL SIGNING DAY HQKeep it right here for all of the latest developments on National Signing Day in Clemson!