The IPO will raise up to $155 million, which the Auckland-based firm will use to fund growth including an expansion of its research and development capabilities.
Orion's technology facilitates the sharing of information between hospital departments, healthcare providers and health professionals.
Orion posted revenue of $153 million in its last financial year but has been making losses as a result of investments for growth.
The company reported a loss of $14.8 million for the six months to September 30 in its IPO prospectus, which did not include any earnings forecasts because the company decided its "lumpy" revenue made providing accurate guidance too difficult.
Ian McCrae, who founded Orion in 1993, is expected to retain a roughly 50 per cent shareholding in the firm following the IPO.