Mr Kim died last week after two women accosted him briefly in a check-in hall at a Kuala Lumpur airport.
Malaysian toxicology reports indicate he was attacked using VX nerve agent, which is classified as a weapon of mass destruction by the United Nations.
There is widespread suspicion that North Korea was responsible for the attack, which it fiercely denies.
It responded furiously to Malaysia's insistence on conducting a post-mortem examination and has accused Malaysia of having "sinister" purposes.
Malaysia's police chief Khalid Abu Bakar said on Friday that the presence of the nerve agent had been detected in swabs taken from Mr Kim's eyes and face.
One of the women Mr Kim interacted with at the airport on 13 February had also fallen ill with vomiting afterwards, he added.
The authorities say they intend to decontaminate the airport and areas the suspects are known to have visited.
Mr Khalid said other exhibits were still under analysis and that police were investigating how the banned substance might have entered Malaysia.
"If the amount of the chemical brought in was small, it would be difficult for us to detect," he said.
Bruce Bennett, a weapons expert at the research institute the Rand Corporation, told the BBC it would have taken only a tiny amount of the substance to kill Mr Kim.
He suggests a small quantity of VX - just a drop - was likely put on cloths used by the attackers to touch his face. A separate spray may have been used as a diversion.
Mr Khalid has previously said the fact the woman who accosted Mr Kim immediately went to wash her hands showed she was "very aware" that she had been handling a toxin.
It would have begun affecting his nervous system immediately, causing first shaking and then death within minutes.
The well-travelled and multilingual oldest son of late North Korean leader Kim Jong-il, he was once considered a potential future leader. He has lived abroad for years and was bypassed in favour of his half-brother, Kim Jong-un.