"We have signed him and we'll release a press release to confirm that he has been signed," Mpengesi tells KickOff.com.
As was revealed by this website last week, the Burundi international was spotted with Chippa when they played to 1-1 draw against Maritzburg United at Harry Gwala Stadium on Friday.
Nsabiyumva, who tried his luck at Ajax Cape Town at the beginning of the season, has been at Cosmos since 2013/14.
The 22-year-old leaves the club having featured in 16 league matches this campaign, with his last game for Ezenkosi coming against Uthongathi FC two weeks ago in Durban.
At Chippa, Nsabiyumva will be reunited with Linda Mntambo and Mxolisi Macuphu who all joined the Chilli Boys in the January transfer window.