Wales face the Wallaroos at the Ballymore Stadium in Brisbane on Saturday, 26 July (05:00 BST) before facing the same opposition at the North Sydney Oval on Friday, 1 August (10:00).
Callender, 24, said: “Playing for Wales has always been an honour and to be asked to lead the squad by Lynny [Lynn] is a real privilege.
“Everybody knows my late mam, Donna, who passed away in 2023, would be so proud to see me lead my country. She has always been my why and I know she is looking down on me and how proud she would be with this news.
“We have had a tough pre-season. We have all put the work in and we are excited to see where we are and measure ourselves against the Wallaroos as we prepare for the World Cup.”
Wales start their World Cup campaign against Scotland at the Salford Community Stadium on Saturday, 23 August (14:45).
They take on Canada at the same venue a week later (12:00) before rounding off their Pool B schedule against Fiji at Sandy Park in Exeter on Saturday, 6 September (14:45).
“Wales has always been a big part of my life, and it was a dream just to play for Wales,” said Williams, who was born in Swansea but grew up in New Zealand.
“To say being asked to be a co-captain of Wales is a proud moment for my family would be an understatement.”
