Te'o and Smith went in succession as the 38th and 39th players chosen, ending a long wait for players who had been two of college football's most highly publicized performers during the 2012 season.
Te'o went to the San Diego Chargers, who traded with Arizona to obtain the No. 6 pick in the second round to get him. Smith, who had been a Heisman Trophy favorite last year before his season took a nosedive, went to the New York Jets.
Te'o finished second in the Heisman Trophy balloting to Texas A&M quarterback Johnny Manziel, but won the Butkus, Lombardi, Bednarik, Nagurski, Maxwell and Walter Camp Awards for his outstanding campaign at Notre Dame.
He recorded 437 tackles in his career, but his reputation took a hit after the season when it was revealed he was the victim of a bizarre hoax involving an Internet relationship with a woman who at first was believed to have died. It was later learned she never existed.
Smith completed his career at West Virginia with 12,004 yards of total offense, having played just 44 games with the Mountaineers.
Only one quarterback was taken in the first round on Thursday -- Florida State's E.J. Manuel being chosen by Buffalo with the 16th pick. Smith was the lone signal caller picked in the second round.
Smith's arrival in New York gives the Jets six quarterbacks on their roster, returning starter Mark Sanchez and Tim Tebow among them.
A running back was finally selected in this year's draft when Cincinnati took North Carolina's Giovani Bernard with the fifth pick in the second round. No ball carrier was taken in the first round, the first time that had happened since 1967.
Eddie Lacy, who gained 1,182 yards and scored 16 touchdowns for national champion Alabama last season, became the 61st player chosen when he was selected by Green Bay late in the second round.
Cornerback Tyraan Mathieu of LSU became the highlight pick of the third round when he was chosen by Arizona as the 69th overall selection. Mathieu, a 2011 Heisman Trophy finalist, was kicked out of the LSU program last August due to a violation of team rules.