In a breaking news alert, state television said 100 people had also been injured in the blasts in the Al-Zahraa neighbourhood of the city, which has been targeted in bomb attacks multiple times before.
The provincial governor of Homs, Talal Barazi, told AFP at least 19 people had been killed in the attacks.
He said the two bombers appeared to have pulled up at the army checkpoint in a car together, with one exiting the vehicle before the other detonated his explosives while still inside.
In the chaos of the first blast’s aftermath, and as a crowd gathered, the second bomber detonated his explosives, Barazi said.
The Syrian Observatory for Human Rights, a Britain-based monitor, also reported the blasts, saying at least 21 people had been killed, among them 13 regime forces.
The group’s director Rami Abdel Rahman said the second suicide bomber had been wearing military clothes.
The Al-Zahraa district of Homs has been targeted in multiple bomb attacks in the past, including in late December, when 19 people were killed in several simultaneous blasts.
The residents of Al-Zahraa are mostly Alawites and the Islamic State group has in the past claimed attacks on the district.
Homs city was once dubbed the “capital” of Syria’s uprising, which began with anti-government protests in March 2011.
But after years of devastating fighting and government sieges, most of the city is now back in regime hands, with the exception of the Waer district, which is being gradually turned over to the government under a deal with opposition fighters.