The 71-test All Black will look to add to the solitary Auckland cap he picked up last season after not being wanted by the national selectors for the Rugby Championship.
Pivac said it was exciting to be able to name Weepu in his squad.
"Piri obviously wasn't in our initial planning so to have him in the team is an added bonus. The experience he brings will definitely come in handy with a young first five-eighths in Simon Hickey outside of him," he said.
Hadleigh Parkes returns from a season with the Southern Kings in South Africa to captain the side, after taking on captaincy duties for most of the 2012 campaign.
Super Rugby players Luke Braid and Sam Prattley are set to make their Auckland debut this season after previous experience with Bay of Plenty and Tasman respectively, while Hickey is one of four players in the squad that played in the New Zealand Under-20 team this season, alongside Joe Edwards, Lolagi Visinia and Patrick Tuipulotu.
Seven members of the squad are set to make their provincial debut for Auckland this season.
"We've spent a lot of time watching an exciting club rugby competition. A number of these young guys have been promoted into this team for the first time because of what we've seen at club level," said Pivac.
Of those set to debut are 18-year-olds So'otala Fa'aso'o and Vince Aso, both members of the 2012 New Zealand Secondary Schools team.
Those not considered due to injury include Gareth Anscombe (shoulder), Albert Nikoro (knee), Ben Lam (foot) and Dave Thomas (shoulder). Also unavailable are Charlie Faumuina, Keven Mealamu, Steven Luatua and Charles Piutau who are all with the All Blacks.
The team goes into camp this week ahead of their second and final pre-season match against Hawke's Bay on Saturday. Auckland's ITM Cup season begins with the 'Battle of the Bridge' against North Harbour at Eden Park on August 18.
The 2013 Auckland ITM Cup team is: Tom McCartney (Pakuranga), Gafatasi Su'a (Ponsonby)*, Nathan Vella (Grammar Carlton), Pauliasi Manu (University), Angus Ta'avao (Marist), Sam Prattley (Pakuranga)*, Ofa Tu'ungafasi (Grammar Carlton), Liaki Moli (Manukau Rovers), Patrick Tuipulotu (Ponsonby)*, Jack Whetton (Grammar Carlton)*, Joe Edwards (Pakuranga), So'otala Fa'aso'o (Grammar Carlton)*, Luke Braid (University)*, Sean Polwart (University), Sean Brookman (University), Peter Saili (Marist), Piri Weepu (Maungarua), Junior Poluleuligaga (Papatoetoe), Wayne Ngaluafe (Ponsonby)*, Simon Hickey (Grammar Carlton), Malakai Fekitoa (Pakuranga), Hadleigh Parkes (Grammar Carlton), Vince Aso (Ponsonby)*, George Moala (Grammar Carlton), Tenina Sauileoge (Papatoetoe)*, Saleaula Silipa (Pakuranga)*, Lolagi Visinia (Suburbs).
* Players named in the Auckland team for the first time.
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