Span will acquire the 30% stake from individual shareholder Mladen Amidzic for 400,000 euro ($433,130), it said in a filing with the Zagreb stock exchange.
The remaining 10% stake is held by Trilix itself, the filing read.
"With this acquisition, Span gains significant intellectual property (IP) from Trilix products and the opportunity to offer their clients services from Span's broader portfolio," Span said.
Trilix will continue to operate as a separate entity within the Span group after the completion of the transaction.
Span's shares traded 4.72% higher at 51 euro on the Zagreb bourse by 11:00 local time on Friday.
($ = 0.924 euro)