The 31-year-old said there was "no violence" during the incident in the early hours of Sunday morning and he is scheduled to fly back to the UK on Monday (local time).
In a statement issued through his English club Saracens, Vunipola said he was charged with resisting the law and fined 240 euros ($A392) following an "express trial".
He described the incident as an "unfortunate misunderstanding" that "got out of hand".
In his statement, Vunipola said: "I can confirm I was involved in an unfortunate misunderstanding when I was leaving a club in Majorca on Sunday, which got out of hand.
"Contrary to media reports, there was no violence, no fight and I did not threaten anybody at any stage, with bottles or chairs or anything else.
"I was charged with resisting the law and, following an 'express trial', I have paid a fine of 240 euros. The Spanish police investigation is now closed, and I am flying back to the UK today.
"I will obviously co-operate with the Saracens internal process and unreservedly apologise for any inconvenience to all involved."
Local reports said Vunipola was tasered twice by police after arriving at a bar in the island's capital Palma in the early hours of Sunday morning.
Saracens tweeted to say they were aware of an incident involving the player and would be dealing with the matter internally.
Vunipola is expected to leave Saracens at the end of this season and has previously been linked with a move to France - although nothing has been confirmed.
Born in Sydney to Tongan parents, the family moved to Wales when Vunipola was a young child after his father, Fe'ao, signed for the Pontypool Rugby Football Club in 1998.
Vunipola has won 75 England caps, making his Test debut against Argentina in 2013. He is not currently part of the England squad.
He made an appearance as a second-half substitute for Saracens in their 15-12 victory over Bath on Friday night.
Saracens are not scheduled to play again until May 11.
They are second in the Gallagher Premiership and chasing a sixth league title in the past 10 seasons, with just two rounds of regular-season games left before the playoffs.
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