After a six hour debate, the lawmakers approved the bill - known as the Convertibility II - into law, effectively establishing a new exchange rate for the entire economy.
The idea is sponsored by Economy Minister Domingo Cavallo, as he struggles to shield his economy from exposure to the US and stabilise the peso.
One peso is now fixed at one dollar and will become fixed to one euro, as soon as the euro rises to parity with the dollar.
When the euro then rises or falls against the dollar, the peso will be set at the mid value between the two currencies.
Seeking stability
The measure is part of a larger package aimed at cutting company costs and boosting growth for Latin America's third largest economy.
Argentina's economy has been in recession for three years.
Mr Cavallo says the new measure is imperative for the peso's stability.
But much smaller changes made to the currency pegging system last week was received doubtfully by the international markets.
International fears
Last Friday Mr Cavallo announced that exporters and importers would be partially exempted from the mechanism by which the Argentine peso is pegged against the US dollar.
Financial markets, sensitive to Argentine policy after a spate of dire economic news, interpreted the move as effectively a devaluation of the peso, and have this week started to pile pressure on other emerging market currencies.
Mr Cavallo has grown increasingly frustrated by the reaction of international markets which he blamed on ignorance.
"The behaviour of the market just shows they did not understand what we wanted to do. But that should not surprise us. They didn't understand [the dollar-peso peg] introduced in 1991," he complained.
The new euro peg approved on Thursday is likely to take many months to come into effect.
The euro is now worth about 85 cents of a dollar.
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