The Chargers took Reese with the 25th pick in the seventh round, the 240th overall.
Reese caught a 55-yard touchdown pass in Baylor's 49-26 victory over UCLA in the 2012 Holiday Bowl at Qualcomm Stadium, home of the Chargers.
There will be ''many more to come,'' said the speedy Reese, who is only 5-foot-10, 170-pounds.
San Diego's first-round pick, TCU cornerback Jason Verrett, had his first Division I interception at Qualcomm, against San Diego State in 2011.
Reese's 21 touchdowns of 40 yards or more were an NCAA and Big 12 record.
''If he can get us a couple of those, it'd be pretty good,'' coach Mike McCoy said.
After the draft ended, the Chargers signed 17 free agents.
Among them were fullback Chris Davis, who came up with one of college football's most memorable plays on Nov. 30 when he returned a missed field goal 109 yards for a touchdown on the final play for a 34-28 win over the two-time defending national champion and then-No. 1 Alabama, and New Haven tight end Michael Flacco, younger brother of Baltimore quarterback Joe Flacco.
The Chargers didn't have a fourth-round pick after trading it to Miami to move up in the second round Friday to take Georgia Tech outside linebacker Jeremiah Attaochu.
Carrethers' last play in college was blocking the potential tying field goal as time expired to preserve the Red Wolves' 23-20 win against Ball State in the GoDaddy Bowl.
General manager Tom Telesco said the 6-2, 330-pound Carrthers has ''uncommon production'' for a nose tackle, citing his 93 tackles, including eight for a loss, and four sacks last year.
''He has extraordinary athletic ability,'' the GM said. ''He's got a real chance here.''
Telesco called Grice ''a well-rounded back'' and ''a touchdown machine'' who scored 39 times in two seasons with the Sun Devils.
Grice, taken with the 25th pick in the sixth round, the 201st overall, rushed for 996 yards and 14 touchdowns last year while catching 50 passes for 438 yards and six touchdowns. A broken leg kept him out of the loss to Stanford in the Pac-12 championship game and the Holiday Bowl.
Also Saturday, Attaochu was introduced at a news conference.
Attaochu moved with his family from Nigeria when he was eight. He played flag football in grade school and wasn't introduced to tackle football until his freshman year, quite by accident.
''I tried to sign up for soccer, walked into the wrong room and the freshman football coach told me to come out and try to play football. From then on I started getting good at it,'' Attaochu said.
''It was an excellent mistake,'' he said.