Mr Parsloe did not clarify how long it would take 235 union members among the company's permanent staff to return to work, but said an agreement was reached on Monday on a process to start on Thursday morning.
The company, which last week refused to allow an immediate return to work from a four-week strike on "health and safety" grounds but relented when faced with Employment Court injunction proceedings, would not discuss what it called a confidential agreement.
It assured the court last week that it would take back permanent staff by Friday at the latest, although it indicated there was not enough work available from reduced ship calls to immediately re-hire casual employees who went on strike.
Although the company's website lists three ships calling this week at the Fergusson container terminal, two others are still due to bypass Auckland and another has had its entire voyage from Melbourne cancelled.
Labour's industrial relations spokeswoman, Darien Fenton, meanwhile intends moving in Parliament today for legislation to be set down for a first reading for council-owned port companies and their subsidiaries to be subjected to official information disclosure laws.
She said her bill would reverse the exclusion of port companies and their subsidiaries from the definition of council-controlled organisations in the 2002 Local Government Act.
Auckland's port dispute had highlighted the need for the companies to be opened to the same scrutiny faced by every other public institution, Ms Fenton said.