He has been fighting extradition since his arrest in 2008 in a joint Thai-US sting operation.
Al Jazeera's Wayne Hay, reporting from Bangkok, said Friday's appeal ruling is "a big disappointment" for Bout.
"I assure you that we will continue to do everything necessary to obtain his return to the motherland"
Sergei Lavrov, Russian foreign minister
"He will be extradited to the United States on two new charges that have been laid, including money laundering and electronic fraud," our correspondent said.
Bout runs a network of air cargo companies in the Middle East, Africa, Eastern Europe and the US.
US officials allege Bout has used that fleet of planes to move weapons around the world since the 1990s.
"This has been very much a diplomatic wrangling as well as a legal one with Thailand, which of course is very reluctant to upset either the United States or Russia," Hay said.
"The court has recommended he be extradited within three months - that is the last legal avenue for Bout. Now it is up to the Thai government to decide whether they will follow through with the decision or ignore the advice of the court and release him."
Sergei Lavrov, Russia's foreign minister, condemned the decision to extradite Bout to the US, and vowed to do everything to obtain his return to Russia.
|Bout, pictured, denies US allegations that he sold weapons to Colombian rebels [AFP]
"We regret what is in my opinion an unjust decision, a political decision that the appeals court in Thailand has taken," Lavrov was quoted as saying by Russian news agencies during a visit to Armenia.
"This decision, according to the information that we have, was taken under very strong pressure from the outside. This is sad. I assure you that we will continue to do everything necessary to obtain his return to the motherland."
Al Jazeera's Neave Barker, reporting from Moscow, said Russia is angry over the decision because Bout is of key interest to Russian authorities.
"The Thai government has been in the middle of extreme pressure from both Washington and Moscow and for the time being it does appear as though the United States has the upper hand," he said.
"But Bout's lawyer has suggested that there could be potential for a prisoner exchange if indeed Bout is convicted in the US.
"So for a man who has caused a significant diplomatic row, it very much could end with a diplomatic solution."
Bout is also accused of supplying millions of dollars worth of weapons to the Revolutionary Armed Forces of Colombia (Farc) rebel group and to countries under UN arms embargoes.
According to the UN and the US treasury department, he has sold or brokered arms that have helped fuel wars in Afghanistan, Angola, the Democratic Republic of Congo, Liberia, Rwanda, Sierra Leone and Sudan.
Bout has repeatedly denied the allegations.