Dallas took Mississippi State's Dak Prescott with the 135th overall pick in the fourth round of the NFL draft Saturday, two days after a failed bid to trade up for another first-round choice to select Paxton Lynch of Memphis.
"This means everything. It was just something I dreamed about," Prescott said. "I ran around the house acting like I was a Cowboys quarterback my whole life, so for it all to come true, it's such a blessing. Just being here with my family, and [owner Jerry] Jones gave me that call, and just the excitement to have my family a majority of Cowboys fans, it was awesome."
The Cowboys did extensive work on Prescott leading up to the draft and had him at Valley Ranch for a pre-draft visit.
Romo missed 12 games with a twice-broken left collarbone last season, and the Cowboys slid from first to worst in the NFC East at 4-12. They went 1-11 without Romo. Kellen Moore was Romo's backup when the season ended, and Jameill Showers spent most of the season on the practice squad.
"It'll be awesome. I'm going to go in there I'm going to work and compete," Prescott said. "I'm going to do the best I can and work as hard as I can and try to outwork everyone there. Pushing Tony Romo, pushing the other guys, Kellen Moore, and just know while I'm doing that I'm making myself better and making my whole team better."
Prescott sees some similarities between Romo and himself. "[Romo] goes out there and he wins a lot of games and always has the Cowboys in position to win a game, and I felt like I did the same thing in college. To come to the Cowboys and learn under him will be exciting."
Prescott set 38 school records with the Bulldogs and is one of two SEC quarterbacks to throw for at least 70 touchdowns and rush for at least 40 in a career. Florida's Tim Tebow is the other.
It's the first time Dallas has drafted a quarterback since taking Stephen McGee of Texas A&M, also in the fourth round, in 2009. And it's just the third quarterback drafted by the Cowboys since 2001. Romo was undrafted in 2003.
Prescott was arrested in March for speeding and driving under the influence, but both breathalyzer tests were inconclusive and he was released on bond.
Earlier in the fourth round, Dallas tried to address its mediocre pass rush, taking Oklahoma defensive end Charles Tapper with the 101st overall pick. Tapper started 38 of 39 games over his final three seasons with the Sooners, recording 15½ sacks and 26½ tackles for loss. He was a first-team All-Big 12 pick by The Associated Press in 2012.
The Cowboys took Ohio State running back Ezekiel Elliott with the fourth overall pick before getting Notre Dame linebacker Jaylon Smith and Nebraska defensive tackle Maliek Collins in the second and third rounds.
Dallas has finished in the bottom third of the league in sacks in recent seasons and won't have any proven pass-rushers when the season starts.
DeMarcus Lawrence and Randy Gregory, second-round picks each of the past two years, will be serving four-game suspensions. Also, Jones said Friday that the team has ruled out bringing back polarizing defensive end Greg Hardy after one tumultuous season with the Cowboys.
ESPN's Todd Archer and The Associated Press contributed to this report.