Gretzky said his role will be determined by Katz and Oilers Entertainment Group CEO Bob Nicholson.
"My investment is going to be time," Gretzky said. "I'm really excited about being involved with the organization, not just for one year, but for years to come.
"As I said, opportunities have come and gone over the last three or four years. Timing has a lot to do with things and organizations have a lot to do with it. I just felt very comfortable with this organization, Bob (Nicholson), working together on the Olympics and (Oilers general manager) Pete Chiarelli is a wonderful man doing a tremendous job with a good coaching staff. I'm just going to be a small part of it and I'm really excited to represent the Oilers and the city in my travels now.
"It's nice to be able to say I'm back as an Oiler. My wife was really strongly encouraging me that this was the place for me to get back into hockey and I'm thrilled that this is the right place."
He said he'll be more than happy to be a sounding board for Chiarelli, if asked.
"Whatever Peter wants, I'm available for him," Gretzky said. "He's a tremendous general manager, he's got a great track record and he's done a wonderful job for the Oilers. That's not for me to interfere with. When the Oilers want me to represent the city, whatever they want me to do, I'm there for them.
"It's a machine that's heading in the right direction. From where I stand now, we'll figure that out as we go along. Hopefully I'm part of that group in the future to help win a Stanley Cup. That's ultimately the goal."
Gretzky said that he'll be spending more time in Edmonton in the future.
"I made it clear to (Katz) that this year was a little more hectic because I didn't plan in August to be doing this full-time," Gretzky said. "I'll be around a lot. As time goes on, I'll spend more and more time in Edmonton and we'll get a place here and we'll spend more time in the city. I'm not running the team day-to-day. That's up to the staff that's in place.
"I'm excited to just be around it and be able to say I'm part of the Oilers."
Gretzky said his role with the Oilers will not interfere with his duties as official ambassador to the NHL's Centennial Celebration.
"When I talked to Mr. Bettman this morning and told him that Daryl and I had struck a partnership, my obligation to the National Hockey League … I'll live up to it," Gretzky said. "I was going to do those events anyway, the outdoor game in Winnipeg, the outdoor game in St. Louis and the All-Star Game honoring the top 100 players in Los Angeles, so it really doesn't have an effect on that whatsoever."