Gordon received a signing bonus of $4 million, highest ever paid by the Royals.
After signing, Gordon was scheduled to be on a late-afternoon flight for Phoenix, where he will join the Royals' Instructional League club at its base in Surprise, Ariz.
Gordon, at a news conference at Kauffman Stadium, said he doesn't have a target date for playing on that field.
"I'm not putting any timetable for me getting to the Majors," he said. "I know it's going to take a lot of hard work and I'll start off at the bottom again ... and, hopefully, it could be a rapid process."
Although there has been speculation that a position change might be in line for Gordon, with rookie Mark Teahen playing regularly at third base for the Royals, Ladnier brushed off that idea.
"He'll play third base," Ladnier said. "There's no thought process in putting him at another position. I think he's going to be a very good third baseman."
Like Teahen, Gordon is a left-handed batter. Billy Butler, a right-handed hitter who was the club's top draft choice in 2004 and 14th overall, was switched from third base to left field at midseason.
Gordon was the highest draft selection in Royals history.
Just where he will play next season in the Minor League organization is not known.
"A lot of it will depend on what we can get accomplished this winter and how much we can get accomplished before Spring Training to get him ready to go," Ladnier said.
"Then we'll determine whether he's ready to go to High Desert or Double-A or somewhere like that. You're probably looking at High Desert but I wouldn't throw out the possibility of him being in Double-A."
High Desert, in the California League, is the Royals' top Single-A club. Their Double-A club is Wichita in the Texas League.
The Arizona Instructional League will run through Oct. 15. Ladnier said he did not know if Major League Baseball could find a spot later for Gordon in the Arizona Fall League, which begins on Tuesday.
Initial plans call for Gordon to continue working out in Arizona and it's possible he might be placed on an AFL "taxi squad" if he's deemed ready, Ladnier said.
Gordon this year hit .372 for the University of Nebraska's College World Series team. He had 19 home runs and 66 RBIs in 253 at-bats.
He also scored 79 runs and walked 63 times with just 38 strikeouts. He had a .518 on-base percentage and a .715 slugging percentage.
He was the winner of college baseball's "triple crown," the Golden Spikes Award, the Dick Howser Trophy and Baseball America's College Player of the Year.
Gordon was selected on June 7 behind the Arizona Diamondbacks' pick of prep shortstop Justin Upton.
Despite the prolonged negotiation process, Gordon said he kept in good physical shape after Nebraska was eliminated in the College World Series.
"I was staying positive. I knew it was going to work out for the best," he said.
"It was kind of hard to see my teammates go off and start playing and doing well but I got to spend a lot of time with my family, something I haven't been able to do over the last couple of years so it was definitely a 'plus' summer. I don't regret it."
While the Royals complete their 100-plus loss season with a game Thursday night at Minnesota and three games at Toronto, Gordon remained optimistic about the club's future.
"I know they've been drafting good players and they have a lot of good, young players. It might take a while but I'm fine with that and, hopefully, I can be a part of that," Gordon said.
"I want to help them rebuild and get back to the success they've had."