The Packers traded up with the Seattle Seahawks to select the cornerback from Louisville with the 18th overall pick of the 2018 NFL Draft.
Green Bay has signed nine of its 11-member draft class, with only second-round selection Josh Jackson and third-round pick Oren Burks remaining
Alexander, who wore his No. 23 Packers jersey to his graduation over the weekend, is expected to provide immediate help for a Green Bay pass defense that finished 23rd in the league in 2017 with 236.8 yards allowed per game.
The 5-foot-10, 196-pound Alexander recorded a 4.38 time in the 40-yard dash at the NFL Scouting Combine in Indianapolis.
Alexander suffered through an injury-plagued junior year in which he sustained a knee injury in the season opener against Purdue and a broken hand in practice in late October. He finished with 19 tackles and one interception in six games.
He entered the season with some preseason All-America honors, coming off a sophomore year in which he intercepted five passes -- two against eventual national champion Clemson -- and was explosive in the return game, including a 69-yard punt return vs. Florida State.