The procedure could take up to two years so an interim economic accord will come into force on January 1.
That deal will allow free access for Montenegrin products to the EU market, in exchange for the progressive opening, over five years, of its markets to European products.
"Montenegro is closer to Europe today," Sturanovic told a news conference, adding that he hoped to launch an official application for EU membership in the first half of 2008.
Montenegro, which has a population of 650,000 people, voted to leave its union with Serbia in May 2006.
Much work remains to bring the former Yugoslav republic in line with EU standards and practices and it is not expected to join the bloc before 2015.
Rehn called Monday's signing "an important milestone" and said it showed that despite lingering problems, the western Balkans was making steady progress towards the European Union.
"We often hear bad news from the western Balkans and we do have serious challenges in the region. That's why it is great to have again good news from and for the western Balkans."
Rehn said the SAA would bring concrete trade and economic benefits and a visa deal due to enter into force in January would bring easier and cheaper access to visas for Montenegrins.
"I trust that this SAA with Montenegro will serve as an inspiration for the other countries of the region too," he told the news conference.