Boronov has now been replaced by Sadyr Japarov, who protesters released from jail the day before.
Opposition groups had earlier seized control of parliament, protesting election results they say were rigged, BBC reported.
Facing mounting pressure, the country's electoral body has annulled the results of Sunday's parliament elections.
The election results had seen parties allied to the country's president Sooronbai Jeenbekov win the largest share of the votes, amid accusations of mass vote-buying.
President Jeenbekov is still in power but has hinted that he is ready to stand down.
He had earlier told the BBC he was "ready to give the responsibility to strong leaders", but refused to say who he had in mind.
The latest announcement comes after days of chaos which saw protesters seizing government buildings and freeing high-profile political detainees - including Japarov, who had been serving an 11-year sentence for kidnapping a regional Governor during an opposition protest seven years ago.
Former President Almazbek Atambayev, who was serving an 11-year sentence for corruption, was also released.
Only four political parties out of 16 had passed the threshold for entry into parliament in Sunday's election. Three of the four had close ties to President Jeenbekov.
The President had indicated he was ready to annul the result, before the official announcement came from the Central Election Commission, which said it had invalidated the election results "in consideration of the political situation in the country".
"The main goal of the protesters was not to annul the election results but to remove me from power," President Jeenbekov had earlier told BBC Kyrgyz in an exclusive phone interview from a secret hideaway.
He urged all parties to return to the "legitimate field" and work together to avoid the political upheavals of the past.
"To solve this issue, I am ready to give the responsibility to strong leaders, no matter which group they belong to. I am even ready to help them," he added.