The charges have been delivered to a Supreme Court judge who must now decide if the case can be sent to the lower house of parliament.
The lower house would vote on whether President Temer should be tried.
Mr Temer has vowed to prove his innocence. He has faced a slew of accusations since taking office last year but these are the first formal charges against him.
The move follows the release of an audio recording in which Mr Temer appears to be discussing bribes in conversation with Joesley Batista, the chairman of the meatpacking company JBS.
If the corruption case reaches the lower house, Mr Temer's coalition believes it can gather enough votes to block the two-thirds majority needed for a trial to be brought against him.
Image caption Protesters taking to the streets earlier in June, calling for Michel Temer to be impeached
However, President Temer is expected to face further charges in the coming weeks, correspondents say.
Mr Temer is deeply unpopular in Brazil but his centre-right party has been able to govern as part of a coalition.
Opposition parties have been demanding snap elections and his impeachment.
Brazilian politics has become engulfed in political scandal in recent years, with a third of Mr Temer's cabinet under investigation for alleged corruption.
Mr Temer's predecessor, Dilma Rousseff, was removed from office following an impeachment vote in the Senate. She was accused of illegally manipulating the budget, a charge she strongly denied.
More about: #Brazil #MihcelTemer
