"We greatly appreciate their listening to the issues that have been raised by our government and many others who have raised this case," Mr Morrison told reporters in Canberra.
"These issues are complex and our relationship with the Thai government, and in particular the Prime Minister Prayut (Chan-o-cha), is very strong, and we thank them for the way that they have engaged with us on this matter."
The prime minister also thanked Australians who have championed al-Araibi's case, including former Socceroo Craig Foster.
Foster, who rallied international support for al-Araibi's cause, including from FIFA and the International Olympic Committee, has thanked the Thai government and everyone who joined his push.
"Many wonderful people stepped forward to help Hakeem," he wrote on Twitter.
"I can't list them, but will thank each of them in time. My thoughts are with Hakeem's wife. Her nightmare will shortly be at an end."
Opposition Leader Bill Shorten also heralded al-Araibi's release.
"We thank the government and people of Thailand for their understanding and compassion," he said.
Al-Araibi is expected to board a flight back to Australia overnight.
"I'm pleased Hakeem is coming home, and I'll be pleased to see him at home when that occurs," Mr Morrison said.
"But until that happens, we will continue to work that process as you would expect us to, not taking anything for granted."
Al-Araibi's arrest was made after Bahrain issued an Interpol Red Notice for his detention on November 7, with Australia later coming under fire for passing on the notice to Thai authorities before his arrival in Thailand for a belated honeymoon.
He denies the charges and says he was playing in a televised match when the police station attack took place.
Al-Araibi, who plays for the semi-professional team Pascoe Vale FC in Melbourne, was granted refugee status and protection by Australia after fleeing Bahrain in 2014.