It is understood the application has been refused because of his links to President Bashar al-Assad's regime.
The decision was made at a recent meeting of senior officials from the Home Office, Foreign Office and Department of Culture, Media and Sport.
The International Olympic Committee is expected to ratify the decision.
"While not unexpected it will still be hugely controversial this, that the British government has decided to refuse his application," said BBC sports editor David Bond.
The board of senior government officials had been assessing Gen Joumaa's application for a while and had reached a decision in the last few days, our correspondent said.
After being informed of the government's decision earlier on Friday, it is the London Games organisers Locog that must now notify the International Olympic Committee (IOC), which has the final say.
Our correspondent said that while the IOC can be "very, very protective of these sorts of issues where politics and sports collide", it was "extremely unlikely" to go against the UK government's ruling.
Oppression and brutality
There has been widespread international condemnation of the Assad regime's violent crackdown on pro-democracy protesters.
The UN says at least 10,000 people have died in Syria since the uprising began in March 2011.
After the massacre of more than 100 unarmed men, women and children in the town of Houla in May this year, the British government suggested members of the Assad regime could be banned from the Games.
Foreign Secretary William Hague said at the time he was "absolutely sickened" by the deaths, which "shine a light to the whole world on the oppression and brutality of the regime".