The RSF are currently withdrawing from this part of the capital by crossing a bridge, Al Jazeera reported.
"Khartoum is free," al-Burhan said in a video, which was published by the Al Jazeera broadcaster.
Led by General Abdel Fattah al-Burhan, the Sudanese army has been making progress in recent weeks. Last Friday, it successfully regained control of the presidential palace.