A Bahraini court sentenced him in absentia to 10 years in prison over claims by Bahraini authorities that he and a group of protesters attacked a police station with petrol bombs during the Arab Spring uprising.
Director of the department's global affairs section, Chatchom Akapin, said Bahrain had requested that the case be dropped.
He eventually made it to Australia, where he was granted refugee status.
Court spokesman Suriyan Hongvilai said that Hakeem al-Araibi, who lives and plays professional soccer in Australia, was being processed for release. He says he faces torture if returned to Bahrain.
Bahrain footballer Hakeem al-Araibi is brought to the Criminal Court in Bangkok on Feb 4 for an extradition request from Bahrain.
JOE ARMAO SYDNEY MORNING HERALDA jubilant Hakeem al Araibi walks out of Melbourne Airport alongside former Socceroos captain Craig Foster
Mr Araibi has said he was blindfolded and had his legs beaten while he was held in Bahrain previously.
Morrison said he was "pleased" with the outcome and thanked the Thai government, as well as Australian football identity Craig Foster for his advocacy on the case. Thai officials had said a trial could be lengthy, depending on how many witnesses are called by each side.
Foreign minister Marise Payne said there were still "a number of steps to go in this process" but said al-Araibi would hopefully be back in Australia in the next day or so.
"We have been informed that Bahrain wants to withdraw the (extradition) request. if they don't want him, we have no reason to keep him here", he told AFP. The Australian government, Fifa and other football bodies have supported his case.
Thailand's Ministry of Foreign Affairs said it had no comment on the case.