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The 17-year-old will now return to action with the squad at this weekend's race in Australia, the penultimate round of the Moto3 season.
Vinales quit his team and returned to Spain on the Friday of the Malaysian event, abandoning his championship hopes and accusing Avintia of being 'second rate.'
While it appeared his relationship would be severed, Vinales has now confirmed he will return at Australia. He confessed his judgement had been clouded by anger - although he added that in such a mindset riding at his maximum would also have proved impossible.
"Firstly I would like to publicly give my sincerely apologies to those that were harmed or affected by my behaviour in Sepang," he said.
"I'm here to come forward, ask for forgiveness and take responsibility for my mistakes.
"I have returned to continue fighting with my Avintia team for the runner-up spot in the championship. There are many people who deserve it: sponsors, technicians and the fans.
"My hasty departure from the Malaysian GP was certainly not good. But with the tension generated by my position in the team, I fell into a state of anger and frustration that was certainly not an ideal state of mind to ride a bike in - especially ride it at the limit.
"I made a mistake, because although I was not mentally prepared to ride the bike, I should not have left the Sepang circuit, or make such statements.
"And so, I apologise for the harm that has been accidentally caused, to all the fans, to the members of my Avintia team, to FTR, Honda, the championship promoters, and especially the sponsors of team."
Vinales currently lies third in the standings, just eight points behind Luis Salom. His tally of seven wins is still the highest any rider has achieved this year.
In missing Sepang, Vinales effectively conceded the inaugural Moto3 crown to Sandro Cortese.
The German already had a comfortable advantage at the head of the standings, but Vinales retained a mathematical chance of taking the title race into the final three rounds.
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