The Detroit native averaged 5.8 yards per carry for his career and will find at least one familiar face in the Lone Star State — Ezekiel Elliott.
Weber is the ninth Ohio State draftee of 2019 and the sixth form the offensive side of the ball.
Ohio State running back says he is being slept on right now
He is the 14th Buckeye to be drafted by the Cowboys and the fourth running back joining Elliott (2016), Michael Wiley (2000) and Ron Springs (1979).
Dallas has also drafted a pair of fullbacks from Ohio State — Nicky Sualua (1997) and Jamar Martin (2002).
Isaiah Prince became the eighth Ohio State player drafted in 2019 when the Miami Dolphins used a sixth-round pick on him Saturday.
Prince, a three-year starter at right tackle for the Buckeyes, is the 202nd overall pick and the second Ohio State offensive lineman taken this year after the Bengals chose Michael Jordan in the fifth round.
Prince was a first-team All-Big Ten pick last season when he also served as a captain.
Offensive line shines in Buckeye victory, and Dwayne Haskins' running continues to supplement attack.
He started 41 games for the Buckeyes, who won a pair of Big Ten championships with him anchoring the right side of the line.
He is the 23rd offensive tackle from Ohio State drafted in the common era and the fifth since 2012.
Prince is the 15th Ohio State player drafted by the Dolphins, who have chosen a Buckeye three years in a row. They picked linebacker Raekwon McMillan in the second round in 2017 and took linebacker Jerome Baker in the third round last year.
The first Dolphins draft pick from Ohio State was Bruce Elia, a fourth-round linebacker in 1975.
The Cincinnati Bengals have drafted a center from Ohio State for the second year in a row.
The team tapped Michael Jordan with a fifth-round selection Saturday, one year after they chose Billy Price in the first round.
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Jordan earned All-America honors last season after replacing Price in the middle of the Buckeyes line.
He started every game in the middle in 2018 after starting for two seasons at guard, including as a true freshman in 2016.
Jordan is the 20th Ohio State player drafted by the Bengals.
That is more Buckeyes than any other NFL team has taken since the Bengals were founded by former Ohio State coach Paul Brown in 1968.
Kendall Sheffield is the first Buckeye off the board on the third and final day of the 2019 NFL Draft.
The Atlanta Falcons chose the Ohio State cornerback with the ninth pick in the fourth round.
He is the sixth Ohio State player drafted this year.
Nick Bosa was taken No. 2 overall by the 49ers, and Dwayne Haskins went 13 picks later to the Redskins.
On the second night of the draft, Parris Campbell, Dre'Mont Jones and Terry McLaurin had their names called.
Demetrius Knox, a Springfield native who went to high school in Texas, announced he has joined the Seattle Seahawks, presumably as an undrafted free agent.
Know was a starter on the offensive line for the last year and a half before suffering a season-ending foot injury in the Michigan game.
According to the Ohio State football Twitter account, receiver Johnnie Dixon and offensive lineman Malcolm Pridgeon signed with the Houston Texans.