"He's operated around the world and I like his style and like him as a person.
"To me, the relationships I have as chair with CEOs is critically important so that was really the key motivation for me going in."
Withers took over as chairwoman of state-owned broadcaster TVNZ in March 2015, and agreed to extend her role until this April.
She said TVNZ had a good succession plan in place and it was a good time for her to step down.
She also planned to retire from the Treasury's advisory board in September, but will remain as chair of Mighty River Power and a director of Australia & New Zealand Banking Group.
She was named chairperson of the year in the 2015 Deloitte Top 200 Awards as well as winning the supreme award at last year's Women of Influence awards for her work championing diversity and gender equality.
"I've got a corporate governance career that goes back to 1997," she said.
"I've chaired Auckland Airport, TVNZ, [and] I'm chairing Mighty River Power so I hope to bring that whole repertoire of skills and experiences to the Warehouse role," Withers said.
"I've had a long association with the company [including as] a director between'98 and 2005.
"The Warehouse is a fundamentally important retailer in New Zealand and is very highly connected to New Zealanders."
Withers also spent two years as The Radio Network chief executive, four years as Fairfax Media chief executive and 15 years as an Auckland International Airport director and chairwoman.
She will take over from van Arkel on September 23, coinciding with the company's full-year result announcement.
Warehouse shares closed up 5c to $2.82 yesterday.