Rehn decided to initial the agreement after being convinced by Bosnian leaders that they would merge the country's ethnically divided police service.
Al Jazeera's Mark Seddon said: "If this latest agreement unravels not only will EU membership be off, but Bosnia could be plunged back into a vicious civil war".
After the three-and-a-half year war ended in 1995 the country divided into a Serb Republic and a Bosniak-Croat Federation, each with its own police force.
Since then, almost all ethnically divided government institutions, including the army have merged so that Serbs, Muslim Bosniaks and Croats serve together.
The EU said it was essential for the police to merge, but Bosnian Serbs argued against a separate police force, fearing it would lead to the loss of their separate territory within Bosnia.
The controversial issue blocked the SAA for a year until the surprise deal but officials in Brussels say the EU will only sign the accord once Bosnia has produced concrete results in its reform pledges.
Luis Amado, the foreign minister of Portugal which currently presides over the EU, said in a speech read by representatives: "We all welcome you to the European family, where you belong".
'Work to be done'
Javier Solana, the EU's foreign policy chief, congratulated the people of Bosnia in a statement but reminded them that there is still "much work to be done."
Prime Minister of the Bosnian Serb mini-state, Milorad Dodik, said the necessary laws could be adopted in December or January, when the agreement could be signed.
However, Bosnia's membership of the 27-nation union is likely to take years to be confirmed.
According to an EU report released last month Croatia is the only western Balkan nation that is likely to be a member of the EU before the end of the decade.
Macedonia, Montenegro and Serbia will need at least five years to prepare themselves economically and politically for membership, the report said.