The technology and administration services provider, which employs 300 people in Northern Ireland, has won a government contract worth £500,000.
Its system is designed to help with the recording, planning and scheduling of staff.
The Passport Office has 2,500 employees working from 37 locations across the UK.
The platform will initially be used in Glasgow and then rolled out to the six other Passport Office locations throughout the UK.
Equiniti secured the deal though the government's G-Cloud procurement framework.
Nigel Farr, one of the company's directors, said: "Working patterns have changed dramatically over the last decade and far fewer businesses operate the stereotypical nine-to-five hours."
"Having a time and attendance system that is cloud-based is increasingly becoming essential in order to accommodate anything from flexible working or remote working to job sharing and hot-desking across locations," he added.
"Her Majesty's Passport Office has increased its flexibility and capability to respond to extreme external pressures which have a direct effect on its workforce requirements."
Belfast-based firm Equiniti has been selected to provide a cloud-based system for the Passport Office.