Mr Joyce said Sir Maarten's strong reputation for "independence, trust and integrity" makes him an ideal person to be involved in the probe.
Mr Jack has extensive experience in reviewing and advising on issues relating to major information technology systems, including the review of security breaches in the Ministry of Social Development's self-service kiosks.
He is also leading the Technical Review of the stability of the Novopay system and the data contained in it, so it made "practical sense" for him to be involved in both the Technical Review and the Ministerial Inquiry, Mr Joyce said.
"My expectation is the Ministerial Inquiry will report by the end of May following the completion of the technical review within the next three to four weeks," he said.
Mr Joyce said while new measures are put in place to address the Novopay issues, the situation is "very complex" and will "take some time to resolve".
"I appreciate how frustrating and time consuming this is for school administrators, principals, teachers and other staff," he said.
"The Government is doing everything it can to resolve the issues as quickly as possible."
Costs for the Ministerial Inquiry are estimated to be around $500,000 and will be met from Ministry of Education's baselines.
The draft terms of reference for the review will be consulted with the sector in the coming days.
The inquiry incorporates the previously scheduled Post-Implementation Review.
"It is important that lessons are learned from the issues with Novopay," Mr Joyce said.
"Following the Ministerial Inquiry, I will ask the Ministry of Business Innovation and Employment to work with Treasury, the State Services Commission and the Government Chief Information Officer to provide Cabinet with advice about contracting arrangements in the wider State Sector."
Besides the Ministerial Inquiry and the Technical Review, other measures the Government is putting in place to address the issues with Novopay include a new Remediation Plan, which will accelerate software stabilisation, monitoring, enhancements and improved customer service; a Ministry of Education re-engagement plan with schools; and investigating a revised Contingency Plan with the previous payroll supplier.