The move to normalise diplomatic ties follows the signing of a peace pact between Jakarta and the Free Aceh Movement (GAM) in August in Helsinki, ending a nearly three-decade separatist insurgency in the tsunami-ravaged province.
The process of selecting of a new ambassador to Sweden will take several months, foreign ministry spokesman Yuri Thamrin said.
"We have to submit names to parliament first," he told AFP.
Jakarta had in the past repeatedly urged the Swedish government to take action against exiled GAM leaders who hold Swedish citizenship, accusing them of directing a campaign of killings and kidnappings in Indonesia.
In response to the pressure, Swedish prosecutors last year raided the homes of three GAM leaders -- self-styled "prime minister" Malik Mahmud, "foreign minister" Zaini Abdullah and co-founder Hasan di Tiro.
But they closed the case against Di Tiro a month later, citing his ailing health and in April dropped the investigation into Abdullah and Mahmud owing to a lack of evidence.
A fourth GAM official, spokesman Bakhtiar Abdullah, has returned to Aceh in the wake of the signing of the Helsinki peace accord.
GAM started fighting in 1976 for the independence of Aceh province, located in northern Sumatra. It has a population of four million and large oil and natural gas reserves.
The peace pact was spurred by the December 2004 tsunami catastrophe, which killed some 168,000 Acehnese.