A report by the International Atomic Energy Agency, concluding that Iran had fulfilled its obligations under the agreement, would come out on Friday, broadcaster IRIB cited Araghchi as saying, paving the way for sanctions to end.
The IAEA findings would be followed by "reaching the end of the line and the announcement of the implementation during Friday, Saturday and Sunday," the official IRNA news agency quoted the minister as saying.
There was no immediate confirmation from the IAEA of Araghchi's comments about the timing of "Implementation Day" when the deal comes into effect, but US and European officials have said it could be just days away.
Araghchi said an announcement about implementation would be made jointly by Iran's Foreign Minister Mohammad Javad Zarif and European Union foreign policy chief Federica Mogherini.
Under its July deal with the P5+1 group -- Britain, China, France, Russia and the United States plus Germany -- Iran agreed to take measures to limit its nuclear activities.
One such step involves making changes to the core of a heavy water reactor at its Arak nuclear site to ensure it cannot be used to make atomic weapons.
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Reports emerged on Monday that Iran had removed the core at Arak, but a top official later denied this was the case, insisting Tehran was still working on a deal to redesign the reactor with the help of China and the United States.
But Araghchi said the new core's redesign would be done by an Iranian company, citing a "reliance on domestic capabilities" to modernise the reactor.
Under the deal, Iran has reduced the number of its centrifuges -- fast-spinning machines that enrich uranium -- and transferred the bulk of its low-enriched uranium stockpile to Russia.
The IAEA must verify that Iran has fulfilled all of its obligations before sanctions can be lifted.
On Monday, President Hassan Rouhani said the country was about to enter "a year of economic prosperity", with sanctions lifted, and said his government had delivered on its promises.
"The government is running the country under sanctions not under normal circumstances. God willing, in the coming days we will witness a rolling up of the sanctions scroll in this country," he said.
On the back of the nuclear deal -- Iran has always denied seeking a bomb -- Rouhani wants to make greater inroads in domestic policy.
But Rouhani has faced criticism from hardline groups about the nuclear deal, with opponents warning it could lead to "infiltration" by the United States.