Three explosions -- two car bombs and a magnetic "sticky bomb" attached to a car -- occurred around one hour apart in the oil-rich ethnically-divided city, security officials said.
The first of the blasts occurred at 9:20 am (0620 GMT) when the "sticky bomb" exploded in the parking lot of the city's police headquarters, Major Salam Zangan said.
When police and emergency responders arrived at the scene shortly afterwards, a car bomb detonated.
"The explosions today killed 25 people and wounded 79 others," said Sadiq Omar Rasul, the director of Kirkuk''s provincial health department. "The majority of the casualties were police."
Earlier, Zangan had put the toll at 18 dead and 70 wounded in two initial blasts, with a security official adding 14 others were wounded in a third car bomb.
The twin blasts caused massive damage to nearby police and civilian vehicles, and several police cars with loudspeakers affixed to them could be heard appealing to Kirkuk residents to make their way to the city's hospital to donate much-needed blood for victims, an AFP journalist said.
At around 10:30 am, another car bomb exploded near the convoy of a senior police official in Kirkuk, Colonel Aras Mohammed.
He and 13 of his bodyguards were wounded in the blast, which also caused serious damage to several nearby cars and buildings, a security official said, on condition of anonymity.