Unleashed has more than 4,000 customers across the UK, EMEA, US, New Zealand and Australia.
The acquisition will add around £9.6M (NZ$18.5M) to the Access Group's revenue.
"Joining Access gives Unleashed a new level of expertise in the provision of integrated software solutions, an acceleration of our product development and gives our customers the opportunity to explore a wider range of ERP and business management solutions from a single provider," said Unleashed CEO Gareth Berry.
"We set out over a decade ago to give businesses the freedom to better make, manage and move products – we believe that 'good products matter' and have championed consumer choice by building the best software with a great team to support our customers to achieve their business potential.
"Our story continues but in an enhanced way as part of The Access Group, and we are really excited to be joining Brendan and the team as part of the Access ERP business."
Access ERP managing director Brendan Flattery said "Our ERP business supports customers across online retail, warehousing, distribution, construction and manufacturing in the UK, EU, Australia, New Zealand and the US with end-to-end enterprise resource planning.
"With the global ERP market expected to reach $49.5B in the next five years, the addition of Unleashed into the Access portfolio gives us a significant opportunity to increase our presence and potential across these sectors. Our integrated approach to software, processes and data enables organisations across the globe to benefit from clarity and control of their inventory, from source to sale.
"We are really excited to be welcoming Gareth, Lisa Miles-Heal and the rest of the Unleashed team into the Access Group."
The acquisition is subject to regulatory approvals but is expected to close in the coming weeks.