Shares in the company, which is due to be listed on Aim on Friday under the ticker PRSM, have been given a placing price of 78p.
Market capitalisation when the company is listed is expected to be around £48.5m, while Investec Bank is acting as nominated adviser and sole broker.
"This is an important step for Blue Prism as we increase the profile of the group in line with the growing awareness of the robotic process automation market," said Alastair Bathgate, chief executive of Blue Prism. "We believe that the IPO will assist our next stage of growth, providing access to capital to fund our expansion plans as well as further incentivise our employees.
"In addition, the increased visibility over our business will help to improve the assurance and confidence our customers and partners place in Blue Prism. This is a very exciting time in the group's evolution and we look forward with confidence to the next stage in Blue Prism's development."