Surayud Chulanont will travel to Brunei's capital early on Thursday and is scheduled to meet with Sultan Hassanal Bolkiah before leaving for Singapore later in the day.
He will hold talks with Singapore's Prime Minister Lee Hsien Loong before returning to Bangkok late on Thursday.
"Prime Minister Surayud will make official visits to Singapore and Brunei on November 9 at the invitation of the governments of those countries," the foreign ministry said in a statement.
Analysts had previously said that a visit to Singapore would be difficult because of its role in Thailand's political crisis which culminated on September 19 with the ouster of premier Thaksin Shinawatra.
Thaksin's family sold their 49 percent stake in Shin Corp., a telecom giant founded by the deposed premier, to Singapore's state-run Temasek Holdings for 1.9 billion dollars under a tax-free deal in January.
The sale triggered months of street protests demanding Thaksin's resignation over alleged abuse of power and corruption, which eventually led to the bloodless coup that removed the billionaire businessman.
But Surayud said on Tuesday night that he had already discussed the controversial deal with Lee on the sidelines of a regional meeting in China late October, and said it was a commercial deal best left to the Thai courts.
"For the Thai government, we are not going to deal with that case directly and we will let role of law do its business," he told a gathering of foreign correspondents on Tuesday night.
A Thai court is due to hear a case against Shin Corp, now under control of Temasek Holdings, for alleged violations of foreign ownership regulations that occurred after the buyout.
Thai finance minister Pridiyathorn Devakula said on Tuesday that if any wrongdoing was discovered, Temasek would have the chance to correct it.
He said that Thailand would not be embarrassed to talk to Singapore, but added: "They will be embarrassed to talk to us".
Surayud last month made a whirlwind diplomatic tour visiting Vietnam, Laos, Cambodia, Malaysia, Indonesia and the Philippines to reassure them that it was business as usual in Thailand despite the recent coup.
He also visited China last month to mark the 15th anniversary of ties between Beijing and the 10-member Association of Southeast Asian Nations, and will go to Hanoi next week for the Asia-Pacific Economic Co-operation summit.
But the premier currently has no plans to visit neighbouring military-run Myanmar.

Copyright AFP (Agence France-Presse), 2006