"Porto has received from Andre Villas-Boas the amount foreseen in the release clause of this employment contract," the Europa League champions said in a statement.
Porto president Jorge Pinto da Costa said last weekend that Villas Boas' release clause was 15 million euros.
The coach, whose contract with Porto ran until 2013, has been linked with Chelsea who are seeking a new manager after sacking Carlo Ancelotti on the last day of the season in May.
Porto had said in a statement earlier in the day that they been informed by Villas-Boas that was quitting and that his contract would be deemed terminated once the deposit for the release clause had been paid.
The Portuguese club appointed Villas-Boas' assistant Vitor Pereira as head coach, with the 42-year-old signing a two-year contract.
Villas-Boas, who worked as assistant and coach at Chelsea under Jose Mourinho from 2004 to 2007, joined Porto as head coach in June last year and led the club to a treble of Portuguese Premier League, Portugal Cup and Europa League.
He also worked under Mourinho at Porto and Inter Milan, before helping Academica Coimbra avoid relegation from the Portuguese Premier League after starting his career as head coach at the club in October 2009.
Villas-Boas had said last month that he planned to stay at Porto next season.
He became the youngest coach ever to win a European club competition when Porto beat compatriots Braga to triumph in the Europa League last month.
His rampant Porto team also became the first side since 1978 to finish the Portuguese league season undefeated, clinching the title with a win at their rivals Benfica's Luz Stadium.
