He identified the deceased students as Oluwaseyi Kehinde, a 100-level student of Crop Science and Horticulture and Joseph Okonofua, a 300-level student of Biology Education.
The student leader said two others were injured and admitted to hospital.
He insisted that the police must be held accountable for the death of the students.
The protest was said to have been caused by blackout at the institution.
The demonstration later degenerated, leading to the killing of two students.
The school management had issued a statement on Wednesday, asking all students to vacate their hostels because the campus had been shut indefinitely.
The state Police Public Relations Officer, DSP Caleb Ikechukwu, in a statement had claimed that the students attacked the convoy of the governor’ wife, Bisi Fayemi.
Ikechukwu also alleged that the students assaulted policemen and damaged a police vehicle.
He denied that the police shot any student at the scene.
However, the SUG president noted that the police were responsible for the death of the two students.
Oluwaseun explained that while Okonofua, aka Icon, was shot in the stomach, Kehinde, a class representative, was shot in the head.
He said, “We finished the peaceful demonstration at 1.40pm. When I was done with a press conference, we discharged all our students by 2 pm.
“I went to sleep at my friend’s place. I was still asleep when I was called around 4 pm that some of our students had been arrested. A student told me that they were arrested at the Ikole campus and the police were bringing them to Oye town.
“I decided to meet the military official that was with us during our protest so we could find a way to bail them. Together with the army official, we went to meet the Oye Divisional Police Officer. The DPO assured us that the students would be released.”
The 300-level Biochemistry student explained that with the assurance, he returned to his friend’s house to continue resting.
He said a few minutes later, his personal assistant called him that the army officer was looking for him.
“I thought it was about bail. When I met him, he said the chief security officer to the governor was around and I should meet him.
“When we got to where the CSO was, we started talking. While I was with him, an officer came from nowhere and slapped me.
“There were students around and that incident almost caused chaos. Everybody queried the officer for slapping me. I was also angry and asked what I did. The army officer and the CSO begged me to be calm.
“They said we should enter the car to go and see the governor and they would ensure that the officer apologised. The students said I should not go.
“Later, they said I should meet with the wife of the governor and that she was around. The students, again, said I should not go,” he added.
Oluwaseun said while the CSO and the army officer tried to appease him, the CSO told him to meet with the state commissioner of police.
“The CSO asked me and the army officer to wait for him for a minute. After a while, I told the officer I wanted to go and rest and that I was no longer angry. I stood to go and meet the CSO to tell him I was leaving.
“As I turned back to leave, we heard a gunshot. Another police officer had shot into the air. The CSO to the governor ran to meet the policeman and asked him why he shot. Before we knew it, they had fired tear gas canisters at us and that was how commotion started.
“The indigenes started throwing stones and students joined them. Everything turned violent as police started shooting at students.
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That was when they killed a student, which aggravated everything. And we later lost another student,” the student leader added.
The SUG leader called for an investigation into the deaths, saying justice should be done.