Documents sent by prosecutors to the court said both men were Chinese nationals from the Muslim Uighur minority.
China has long faced criticism for the perceived harsh restrictions it places on religion and culture in Xinjiang, where the majority of Uighurs live.
Thailand recently found itself in the spotlight following its forced repatriation of more than 100 Uighurs to China.
Police have released warrants for a total of 17 people over charges stemming from the attack. They believe many have fled the country.
The motive for the bombing remains unclear.
The Erawan shrine - with its four-faced golden statue of the Hindu god Brahma - is considered sacred by Thai Buddhists, and attracts many foreign visitors.