Lai Sai-ming, who captained the Sea Smooth in the 2012 collision, was also found guilty of endangering the safety of others at sea.
The skipper of the other boat involved was acquitted of manslaughter.
Chow Chi-wai - captain of the Lamma IV, which half-sank - was also found guilty of endangering the safety of others.
The crash was Hong Kong's worst maritime accident since 1971.
Lai, 56, was convicted on all 39 counts of manslaughter by seven of the nine members of the jury at the Hong Kong court after nearly 35 hours of deliberations, reported the South China Morning Post (SCMP).
He could face life in prison when sentenced - which his lawyer says will take place on Monday, AFP news agency reported.
Chow, 58, was acquitted by eight to one of the manslaughter charges but found guilty of one count of endangering the safety of others at sea.
Both captains pleaded not guilty at the hearing, which went on for more than 60 days.
Chow's lawyers, the SCMP reports, had argued that his efforts to avert the collision were thwarted by the more manoeuvrable catamaran skippered by Lai.
They asserted that the Lamma IV had turned right three times by about 50 degrees in accordance with international rules, while the Sea Smooth violated the rules and turned left by 21 degrees.
The accident happened on 1 October, China's National Day, when the Lamma IV was carrying employees of Hong Kong Electric and their families - including children, several of whom died in the tragedy - to watch a firework display.
The Sea Smooth was a Hong Kong and Kowloon Ferry passenger vessel.
An inquiry following the collision found safety standards on the Lamma IV - which partially capsized - had not been properly enforced and there had been a "litany of errors".
1. Hong Kong Electric boat departs power plant for firework display in Victoria Harbour
2. Ferry departs Hong Kong island on regular route to Lamma Island
3. Collision occurs north of Lamma Island. Damaged ferry continues to port at Yung Shue Wan. Lamma IV sinks.
The captain of a ferry involved in one of Hong Kong's worst sea disasters has been convicted of manslaughter over the 39 people who died.