Two civilians and a police officer were killed in the blasts, police spokesman Fred Enanga told reporters at a news conference in the city. Three suicide bombers also died.
Police have yet to determine the total number of victims, as a team of forensic experts is still documenting the scene, Enanga added.
The two explosions shook the city center within five minutes of each other. Police said CCTV footage showed an adult man wearing a backpack detonating at 10:03 am local time near the central police station. Enanga said the attacker died instantly.
Two people were confirmed dead at the site of the first blast, while 17 others were critically injured, Enanga said in a statement.
Three minutes after the first blast, two suicide bombers on motorcycles were seen detonated near the Raja Chambers and Jubilee Insurance Building along central Kampala Parliament Avenue, Enanga said. The two attackers were killed and the body of a civilian was also found at the scene, he added.
Enanga said 33 people were injured in the two blasts; five of them are in critical condition. The injured are being treated at the Mulago National Reference Hospital.
Police pursued a fourth attacker, Enanga said, adding that two more bombs were recovered from his home that will be detonated safely.
Enanga said the attacks bore the hallmarks of the Allied Democratic Forces (ADF), an Islamist rebel group.
He urged the public to remain vigilant, warning that: “bomb threats are still active, especially from suicide bombers.”
Traffic in Kampala has been severely restricted after the explosions, and authorities urged the public to close businesses and leave the area.
The police and the army cordoned off the streets around the scene of the blast and several ambulances were deployed.
Images on social media showed several people lying on the streets near the entrance to the central police station and the Kampala High Court.
On Parliamentary Avenue, where the second explosion occurred, all streets have been cordoned off for security, with lawmakers and parliamentary staff evacuated.
Correction: This story has been updated to clarify that two civilians and one police officer were killed, not three police officers as noted above.