"This is a dream come true for me," Okung said. "I'm blessed to be in this position and I have so many people to thank for getting me here.
"There has been so much attention and anticipation the last couple of weeks and I actually feel relieved. Being drafted is the first step to where I want to end up," Okung added.
New Seattle Seahawks head coach Pete Carroll and first-year general manager John Schneider made Okung the team's first choice in hopes that he will follow in the footsteps of six-time Pro Bowl offensive tackle Walter Jones.
Jones, however, is 36 years old and is expected to retire following two knee surgeries.
Jones was the last offensive lineman selected in the first round by the Seahawks, and ironically was taken with the sixth overall pick in the 1997 NFL Draft.
Okung started 47 consecutive games for the Cowboys over the last four seasons, including 39 in a row at left tackle.
"We are very proud of what Russell accomplished during his career at Oklahoma State and what he will now go on to accomplish as an NFL player," said Oklahoma State head coach Mike Gundy.
"He is very mature both on and off the field and he has made a great impact on our program," Gundy continued. "We're excited about what the future holds for him."
Okung elected to return to Oklahoma State for his senior season although he was a highly-ranked NFL prospect after his junior year.
"Coming back for my senior year was a great decision because not only did I get to be part of one of the best teams ever at Oklahoma State, but I also got my degree in business administration and got to enjoy college life for one mor eyear. I'd make the same decision again," he said.
Okung becomes just the second OSU offensive lineman selected in the first round of the NFL Draft. Former Cowboy John Ward was selected with the 25th overall pick by the Minnesota Vikings in 1970.