Emma Madigan was received by Pope Francis, the Vatican said in a statement.
The embassy shut in November 2011, ostensibly for economic reasons.
But the move was interpreted in Vatican diplomatic circles as a snub by Ireland, which accused the Holy See of trying to cover up and interfere in a report on clerical paedophilia.
The sex abuse scandal which rocked the Roman Catholic Church affected huge number of victims in Ireland, where religious leaders were accused of having protected predator priests and disrupted enquiries.
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He said the Cloyne Report "exposed the dysfunction, disconnection, elitism and narcissism" in the Vatican.
The Vatican denounced the actions of offending priests in Ireland but denied having tried to interfere in the report.
The scandal hit the Church hard in Ireland, where the majority of people say they are Catholic but church attendance numbers have dropped.