The rebels have been making advances in the Deir el-Zour province recently, and the capture of the base followed the seizure of a military airport in the same area last week.
In the country's north, meanwhile, the two sides have been locked in a deadly stalemate for months.
Syrian warplanes flattened a building next to a hospital in Aleppo late Wednesday, killing at least 15 people, including a doctor and three children, and damaging one of the last remaining sources of medical help for civilians in the northern city, activists said.
Rami Abdul-Rahman, chief of the Syrian Observatory for Human Rights, said at least 11 fighters were killed in the raid, in addition to a doctor, a young girl and two children who were on the street.
Another activist group, the Local Coordination Committees, confirmed the bombing and identified the doctor as Mohammad Qassem Agha. The group said 40 people died in airstrikes in Aleppo on Wednesday, but did not say how many died in the hospital strike.
Activist groups and a local fighter say the Mayadeen base fell in the morning hours, after a three-week siege. The fighter spoke on condition of anonymity because of security concerns.
The base was considered the last stronghold for regime forces in the eastern province, according to the Observatory.
In Damascus, two mortar shells struck the upscale neighborhood of Mazzeh during the morning rush hour yesterday, injuring at least one person, Syrian state TV said.
The report blamed "terrorists" for the attack, a term the government uses for opposition fighters.