Also charged will be Abhisit's former Deputy Prime Minister Suthep Thaugsuban, a report by the Bangkok Post said.
The driver was shot by soldiers during anti-government protests that turned violent, the Post reported.
More than 90 people died and more around 2,000 people were believed injured during clashes with police and security forces in April and May 2010. The fighting took place between security forces and supporters of ousted former Prime Minister Thaksin Shinawatra -- called Red Shirts -- as well as those of the United Front for Democracy against Dictatorship.
Supporters of Abhisit are called Yellow Shirts.
Tarit Pengdit, director general of the Department of Special Investigation, said the charges against Abhisit and Suthep would be the first legal charges over the deaths.
Abhisit and Suthep are to report to the DSI Dec. 12 to acknowledge the charges.
Tarit said they would be released without conditions after reporting, a procedure that is in line with the Criminal Procedures Code and the Special Cases Investigation Act, because the two men were former holders of high-level political offices.
The Criminal Court recently ruled that Phan, the taxi driver, was killed by bullets fired by soldiers on the orders from the Center for the Resolution of the Emergency Situation.
The Post report said Suthep was the ultimate commander of the CRES, with Abhisit as his superior.
Tarit said no soldiers would be charged because it wasn't determined who fired the fatal shots.
In July 2011, Abhisit resigned as leader of the Democrat Party, which had just roundly lost the country's hotly contested general election. His party was crushed by its main rival the Pheu Thai Party, led by the neophyte politician Yingluck Shinawatra, 44, and sister of former controversial Prime Minister Thaksin Shinawatra.
Critics of Yingluck -- Thailand's first female prime minister -- say real government power lies in Dubai where Thaksin lives in self-imposed exile.
Thaksin, 61, was ousted in a military coup in 2006 and soon after was sentenced to two years in prison for tax fraud. He fled in 2008 rather than serve his sentence, leaving an estimated $2 billion in frozen assets.
The two-month extent and high number of deaths in the 2010 riots forced the government to set up a Truth for Reconciliation Commission.
Earlier this year the Thai government acceded to recommendations from the commission to set up a compensation fund of around $63 million, the BBC reported at the time.
The fund covers families of the deceased, as well as those who were hurt or "unfairly detained," the BBC said.
Monies are for funeral costs and for getting medical help for psychological trauma.