The move will give him more direct control over the talks, which have until now been conducted by the Supreme National Security Council.
The council is appointed by and answerable to the Supreme Leader, Ayatollah Khamenei.
Correspondents say the change could herald a less hardline Iranian stance in the talks.
The change had been rumoured for several weeks.
Western countries fear Iran wants to develop nuclear weapons – a claim it denies.
Since 2007, Iran’s delegation at nuclear negotiations has been led by Saeed Jalili, who was seen as highly loyal to Mr Khamenei.
Mr Jalili also stood as a presidential candidate at this year’s election, on a platform perceived as espousing an aggressive policy abroad and limited political openness at home.
The move makes it likely that Foreign Minister Mohammad Javad Zarif will take over responsibility for talks.
Mr Zarif has experience living in and negotiating with the West, having previously been Iran’s envoy to the UN, and is viewed as a political moderate.
‘Lack of progress’
Last week, a report from the UN’s nuclear agency said Iran had further boosted its capacity for uranium enrichment.
The International Atomic Energy Agency (IAEA) said Tehran has now installed more than 1,000 advanced centrifuges at its Natanz enrichment plant.
The IAEA says it will resume talks with Iran on 27 September – the first such negotiations since Mr Rouhani was elected.
In June, IAEA director general Yukiya Amano complained of a lack of progress during 10 rounds of negotiations between Iran and the so-called P5+1 – the US, UK, France, Russia, China plus Germany – despite intensified discussions.
The country has been the target of four rounds of UN sanctions and numerous UN Security Council resolutions calling on it to cease enrichment work amid fears it aims to develop nuclear weapons.
Iran has refused to obey, saying it intends to enrich only for power station fuel or other peaceful purposes.