"It was like, 'Thank you, Jesus,'" Peterson said of his reaction to seeing the breaking news on TV, according to ESPN's Josh Weinfuss. "He answers prayers."
The move came after a hugely disappointing first month with the New Orleans Saints in which the veteran back rushed for just 81 yards in four games.
While Peterson is happy to be out of New Orleans after signing with them in free agency, he insisted he didn't push for the trade.
"I'll be lying to you to say that I didn't want a change of scenery after four weeks of seeing how things played out," Peterson said. "So, yeah, it was something that I was praying about - 'Hey, God, I need you to answer this prayer for me. Are you listening to me?' But in the midst of that, I was still tuned in and locked in.
"I had a great day of practice Monday, great day of practice. It was hot, too. It was outside. It was a good day. It was rough, but I was still locked in and taking care of my business, and the prayer was answered."
Free from the Saints' logjam at running back, Peterson will be the featured back in Arizona - at least until David Johnson returns, which head coach Bruce Arians said Wednesday could happen by Thanksgiving.
Arians said Peterson was able to do "everything" at practice Wednesday, adding the former NFL MVP will be "ready to go" for Sunday's matchup with the Tampa Bay Buccaneers.