He won some 62.6% of the vote in an election marked by a high turnout of 85%, official figures show.
Supporters of pro-reform candidate Mir Hossein Mousavi have cried foul and clashed with riot police in Tehran, despite a ban on public protests.
Iran's Supreme Leader congratulated Mr Ahmadinejad on his win, and urged his rivals against "provocations".
In a statement, Ayatollah Ali Khamenei praised the high turnout and described the count as a "real celebration" and called for calm in the aftermath of the result.
Correspondents say this is the worst public violence for a decade in Tehran.
Four police motorbikes were set on fire near the interior ministry, the BBC's John Simpson in Tehran says.
The authorities had earlier sealed off Mr Mousavi's campaign HQ, preventing his supporters from holding a news conference.
Interior Minister Sadeq Mahsouli said that any demonstrations needed official permission, and none had been given.
The AFP news agency quoted a senior police official as saying: "The time of dancing and shouting is over."
One opposition newspaper has been closed down and BBC websites also appear to have been blocked by the Iranian authorities.
Mr Mousavi was hoping to prevent Mr Ahmadinejad winning more than 50% of the vote, in order to force a run-off election.
However, Interior Minister Sadeq Mahsouli said his share of the vote was 33.75%
source : bbc.co.uk
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