And as expected, he hired Todd Bowles as defensive coordinator.
The addition of the 74-year-old Moore is intriguing.
He has 34 years of experience as an NFL assistant, 12 as Peyton Manning's offensive coordinator in Indianapolis.
He will serve as Arians' assistant head coach/offense. Goodwin, offensive line coach for the Colts last season and an assistant with Pittsburgh five years before that, will be Arizona's offensive coordinator, although Arians will call the plays.
Bowles comes from Philadelphia, where he was promoted from secondary coach to defensive coordinator with Philadelphia on Oct. 16.
In Arizona, he replaces Ray Horton, who left when Arians was hired and is the defensive coordinator for the Cleveland Browns.
Arians, 60, was hired Thursday night to replace Ken Whisenhunt, who was fired after six seasons with the Cardinals.
An NFL assistant for two decades, Arians got his first head coaching gig after going 9-3 as interim coach in Indianapolis when Chuck Pagano was out for treatment for leukemia, helping engineer a stunning turnaround as the team, behind rookie quarterback Andrew Luck, went 11-5 and earned a playoff berth a year after going 2-14.
Such a turnaround would be a blessing in Arizona, where the Cardinals went 5-11 last season, losing 11 of its last 12. Unfortunately for the Cardinals, Arians can't bring Luck with him.
Monday's moves came as Arians headed a Cardinals contingent to scout players, presumably a quarterback or two among them, at the Senior Bowl.
Moore's long resume includes three Super Bowl wins — in 2006 as Colts offensive coordinator and as receivers coach for the 1978 and 1979 Steelers.
After 13 seasons as a college football assistant, Moore came to the NFL in 1977 as receivers coach of the Steelers, then was Pittsburgh offensive coordinator from 1983 to 1989. He was assistant head coach at Minnesota from 1990 to 1993, offensive coordinator at Detroit from 1994 to 1996 and running backs coach at New Orleans in 1997.
Moore came to Indianapolis in 1998, the year Manning arrived as a rookie. The two were together through 2011. When the Manning era ended, Moore left the Colts and became an offensive consultant to the New York Jets, then had the same job with the Titans.
Arians worked with Moore and Manning as quarterbacks coach in Indianapolis before leaving in 2001 to become offensive coordinator in Cleveland.
Bowles' connections with Arians go back even further. In 1985, Bowles was a team captain at Temple, where Arians was head coach. Bowles played defensive back for eight NFL seasons with the Washington Redskins and San Francisco 49ers. He was a member of the Redskins team that won the 1988 Super Bowl.
Bowles was secondary coach for Dallas for three seasons, then moved on to the same job with Cleveland and the New York Jets. Bowles, 49, was assistant head coach-secondary coach with the Miami Dolphins from 2008 to 2011, serving briefly as interim head coach when Tony Sparano was fired late in Bowles' final season there.
He joined Andy Reid's staff in Philadelphia as secondary coach a year ago and was promoted to defensive coordinator on Oct. 16 when Juan Castillo was fired.
Bowles will bring a different system than the 3-4 employed by Horton, who in two seasons in Arizona developed a defense that led the league in several categories.
Horton was a candidate for the Arizona job, but there was no chance he was going to stick around when Arians was hired. He took the Cleveland job within hours of the announcement of the Cardinals' hiring.
Goodwin's background with the offensive line will come in handy in Arizona, where the unit was a problem much of the season although rookie tackles Bobbie Massie and Nate Potter did improve as the season progressed.
He came to the NFL as an assistant offensive line coach in Chicago in 2004. Goodwin's brother Jonathan is the starting center for the Super Bowl-bound San Francisco 49ers.
No. 1 on the new staff's priority list is finding a quarterback. Kevin Kolb is the only one on the roster who had any success last season, but both of his years in Arizona have been cut short by injury. He's due to make $9 million, plus a $2 million roster bonus, this year so he probably would have to rework his deal in order to return.
The other options are free agency and through the draft. Arizona has the No. 7 overall pick, but most who know about such things doubt that any quarterback is worth that high a pick this year, especially with Arizona's big needs on the offensive line.
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