"It was understood to me that I was going to be the No. 2 and come in and compete and do what I've done over my career," said Anderson, who agreed to a two-year deal with the Cardinals on Wednesday. "I am coming into camp and everything like that, and I've gone into every training camp I have been involved in thinking I am going to play and get better. Obviously, my job will be to push Matt and make him better, too."
Leinart had been the only quarterback on Arizona's roster following Kurt Warner's retirement last month.
"We have seen a tremendous amount of growth from Matt. He has worked hard," Cardinals coach Ken Whisenhunt said Wednesday, "but I am also excited about Derek, and there will be competition at that position. That's not anything different than what we have at other positions."
Anderson spent five up-and-down seasons with the Cleveland Browns, and he lost his starting job to Brady Quinn at the start of last season. Anderson got the job back, lost it, then got it back again when Quinn was hurt. The Browns released Anderson last week.
"I think a fresh start was something that I wanted," Anderson said in a conference call, "getting out of Cleveland and getting out there and compete and kind of prove that I can play. 2007 was a great year, but the last couple of years haven't been, obviously, good for me or the team I was playing on. So I am just excited about a new opportunity with a new team."
Anderson -- who took a parting shot at Cleveland fans when he was released, then apologized -- hopes the new scenery will turn things around for him.
"New coaches, new everything, new life, kind of start over a little bit will be good," Anderson said. "Obviously, like I said, the receivers and the skill-position guys that they have was something that I thought was a big thing about coming down there."
Leinart, the former Heisman Trophy winner at USC, lost the starting job to Warner in 2008 training camp. Warner, of course, went on to lead the Cardinals on an improbable run to the Super Bowl that season, then directed the team to a second consecutive NFC West crown and the second round of the playoffs last season.
Whisenhunt said he received a text from Leinart on Wednesday saying he "knew there was going to be competition, but he was going to show he was ready to play."
"So that indicated to me that Matt was in a good place," the coach said. ".... I don't know necessarily that it was a function of any announcements about us reaching an agreement with Derek as much as it was just Matt staying in communication. That is what we want from our players, and I was excited to see that."
The Associated Press contributed to this report.