The deal will see Peugeot work with the manufacturer Iran Khodro, with the first vehicles expected to roll off the production line in 2017.
It makes Peugeot the first Western carmaker to announce a return to Iran since sanctions were lifted against the country after it signed a deal to limit its nuclear programme.
Peugeot and its French partner Citroen will work with Iran Khodro to produce 200,000 vehicles a year using parts manufactured in Iran.
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The aim is to produce the Peugeot 208, the 2008 sport utility vehicle and 301 compact models.
Peugeot pulled out of Iran in 2012 as Western sanctions imposed over the Islamic Republic's nuclear programme began to bite.
At the time, Iran was Peugeot's second-largest market after France.
With the lifting of the sanctions, Iran has signed a raft of commercial deals and Rouhani is also expected to tie up an agreement to buy more than 100 passenger jets during his two-day visit to France.