Seattle has made just two picks through the first two days, getting running back Rashaad Penny from San Diego State in the first round and defensive end Rasheem Green from Southern California in the third round.
"Doesn't feel like real life".
If Dickson does earn the starting job, he should become a valuable asset the Seahawks defense.
Dickson was named MVP of the Texas Bowl after one of the best single-game punting performances in recent college history.
After making such an impact, Dickson chose to forgo his senior year at Texas and enter the National Football League draft. No kicker came off the board before Dickson, making the Australian the first special teams' player chosen in the draft. Seattle ranked No. 17 in the nation in punting average in 2017, and No. 10 in punts inside the 20.
He had a strong showing at the National Football League draft combine and some analysts predicted Dickson's value could have seen him drafted as high as the third round.
Dickson was the first punter picked in this year's draft, and the first Longhorn specialist to be picked since kicker Jeff Ward in 1987.
Prior to the draft, the Oakland Raiders and Seattle Seahawks were the two teams most likely to seek a new punter.
Marcell Ateman's wait was longer than many thought, but the Oakland Raiders selected Ateman in the seventh round with the 228th overall pick.
A native of Australia, Dickson will be replaced at Texas by freshman Ryan Bujcevski.