But a challenge filed by prosecutors against his sentence -- which was far higher than the one-year suspended jail term they had recommended -- will still go ahead.
Basuki Tjahaja Purnama was jailed this month for insulting the Koran while campaigning for re-election, a shock decision that stoked concern about rising religious intolerance in the world's most populous Muslim-majority nation.
The blasphemy allegations against Purnama, Jakarta's first non-Muslim governor for half a century and first ethnic Chinese leader, sparked mass protests spearheaded by radicals. They contributed to him losing last month's vote to lead the capital to a Muslim challenger.
His wife Veronica Tan said the decision had been taken to try to end the drama that has divided Indonesian society in recent months.
Rallies and candlelight vigils in support of Purnama, known by his nickname Ahok, have been held across Indonesia and in cities around the world since his conviction.
Tan read a letter written by Purnama from behind bars, in which he said he had dropped his appeal "for the sake of our people and nation".
"What a loss the citizens of Jakarta would have to endure -- congestion and economic losses due to demonstrations that disrupt traffic. It is not appropriate," the letter said.
"Ahok is not afraid," he said, adding that the decision was taken for the "public interest".
The governor was hauled into court last year to face trial for allegedly insulting Islam. He offended Muslims after quoting a passage from the Koran, saying his opponents were using the words to trick people into voting against him.
Some interpret the verse as meaning Muslims should not vote for non-Muslim leaders.
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