Flight QZ8501 plunged into the ocean in stormy weather on December 28, during what was supposed to be a routine flight from the Indonesian city of Surabaya to Singapore.
The crash of the Airbus A320-200 triggered a huge international search, with ships and aircraft from several nations involved in a lengthy hunt that was hampered by strong currents and bad weather.
The bodies of 56 of those who died have never been found.
Cracked soldering in the component caused it to malfunction and send repeated warning messages to the pilots, it said.
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In response, they tried to reset a computer system but in the process turned off the plane's autopilot, sending it into a sharp roll from which they were unable to recover.
"Subsequent flight crew action resulted in inability to control the aircraft," said the report. The plane went into a "prolonged stall condition that was beyond the capability of the crew to recover", it said.
Investigator Nurcahyo Utomo said that AirAsia pilots flying Airbus aircraft had not received adequate training for when their planes became severely destabilised, as it was not recommended by the manufacturer.
The report said the faulty component, the Rudder Travel Limiter, had suffered 23 problems in the past 12 months, citing maintenance records.
"The investigation found some inadequacy in the maintenance system, leading to the unresolved, repeated problem" with the rudder system, said Utomo.
Family members of those killed in the accident had been waiting anxiously for the report, and Eka Santoso -- whose brother, sister-in-law and their two children died in the crash -- urged AirAsia to take action following its recommendations.
"AirAsia must find the people who were responsible for this problem," he told AFP, referring to the faulty competent, and adding those who failed to fix it should be prosecuted. "It has been proven there was a weakness.