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Export levies will return to the fixed rates that existed before March, said cabinet chief Alberto Fernandez.
The Senate had narrowly rejected the government's proposals in a vote following more than 16 hours of debate.
Farmers said the taxes would be crippling, but the government said they were needed to fight poverty.
The tax on farm exports was intended to fund the building of schools, roads and hospitals but strikes by farmers led to food shortages in some parts of the country and a political crisis.
The BBC's Daniel Schweimler in Buenos Aires says that the president had little choice but to scrap the tax increases following the dramatic Senate vote on Thursday.
Senators were tied 36 to 36 after more than 16 hours of debate, until the Vice-President, Julio Cobos, cast the deciding vote to reject his government's proposals.
Our correspondent says it is the first sign of any weakness or backwards step shown by the government, which is often criticised for its intransigence.
Argentina's farmers are delighted by the move, our correspondent adds.
'A hungry world'
Argentina is a major producer of soya, grains and beef, which fetch high prices on international markets.
The dispute between the government and farmers began in March, when President Fernandez's government raised taxes on soya exports from 35% to 45%, and imposed new taxes on other farm exports.
The government argued that they needed to raise taxes on agricultural exports to help build a new Argentina.
It said farmers could afford to pay more, as they were benefiting from high prices.
The authorities also accused farmers and their supporters of undermining democracy by refusing to respect the wishes of the elected government.
However, farmers' leaders said that any profits needed to be reinvested so that Argentina, one of the world's leading agricultural producers, could help to feed a hungry world.
(BBC)
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