The team confirmed the hiring in a release Thursday night, saying Arians received a four-year contract with a club option for a fifth year.
The 60-year-old longtime assistant went 9-3 as Colts interim head coach while Chuck Pagano was undergoing treatment for leukemia last season.
Arians arrived in Arizona on Wednesday night, had dinner with top team officials, then interviewed on Thursday and met with reporters to indicate his interest in the job.
He was offered and accepted the job Thursday night. Arians also was a finalist for the Chicago job that went to Marc Trestman.
Whisenhunt was introduced on Thursday as the offensive coordinator for new head coach Mike McCoy in San Diego.
The team posted a photo of Arians getting a congratulatory call from Cardinals wide receiver Larry Fitzgerald, who is vacationing in Belize and undoubtedly will welcome anyone who can do something to revive a dreadful offense.
“I hope it answered all the questions everybody else has had for all these years,” he said.
It apparently did for the Cardinals, who lost 10 of 11 this season to finish 5-11 for the second time in three years.
Arians said there are young coaches for teams still in the playoffs that will be denied a chance to be a head coach now because of their teams’ success.
“Maybe I was a victim of that a couple of times,” he said. “Hey, I’ll take the Super Bowl ring and look back later. You can’t worry about why you never got one or why have you got one this time. I’m just happy it happened, and I look forward to seeing what’s made of it and what turns out.”
Arians has been a football coach since his days as a graduate assistant at Virginia Tech in 1975 and he has 20 years of experience as an NFL assistant. He also was head coach at Temple for five seasons.