The as-yet unnamed Auckland side was last month granted a licence to become the ALM's 13th team from the 2024/25 season, with a women's side to follow a year later.
"I am really excited about joining the new Auckland A-League club," said Corica.
"It has all the ingredients needed to succeed, both on the pitch and in the community.
"We want to build a club that is known for its attacking and entertaining style of football and Aucklanders are proud to call their own."
The appointment follows that of Sydney FC stalwart Terry McFlynn, who was named head of football earlier this month.
Bill Foley, the US billionaire behind the NHL's Vegas Golden Knights, owns the new team, which joins the Wellington Phoenix as one of two New Zealand-based ALM sides.
Corica indicated Auckland could serve as a breeding ground for Premier League outfit Bournemouth and Lorient in France's Ligue 1, both of whom are backed by Foley.
"Bill Foley is passionate about creating pathways for young talented Kiwis to firstly succeed in the A-League and then go overseas with the other clubs in the group," Corica said.
"It's a fantastic opportunity for everyone involved."
Under Corica's watch, Sydney were back-to-back A-League champions in the 2018/19 and 2019/20 seasons, winning the premiership in the latter campaign.
The Sky Blues sacked Corica in early November after they began his sixth season in charge with three consecutive defeats.
It ended an association with the club that had dated back to its inception; Corica played 106 games for Sydney between 2005 and 2010.
At international level, Corica scored five goals from 32 Socceroos appearances.
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