Amari made the announcement in a televised news conference where he explained results of an independent inquiry into the allegations.
The scandal surfaced after the magazine Weekly Bunshun reported that Amari and his aides accepted at least 12 million yen ($103,000) in cash and hospitality from the unnamed construction company.
As economy and fiscal minister, Amari was one of the most trusted members of Prime Minister Shinzo Abe's Cabinet and served as Japan's top negotiator for the 12-nation Trans-Pacific Partnership trade pact. His resignation comes amid mounting signs Japan's economic recovery is faltering.
Amari has denied any wrongdoing. But he apologized for causing "concern and trouble" and said he felt responsibility for undermining public trust in the government.
During questioning in parliament, Amari said he did not recall clearly the details of meetings in his office with the construction company.
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