Weiss will cost Kiev a transfer fee of ?4million and the official announcement could be made as early as Tuesday, sources have told Sky Sports.
The Slovakia international, who has been at City since 2006 and developed at the club's youth academy, has failed to cement his place in the first team at the Etihad Stadium since making his debut in 2009 and played on loan for Rangers last season.
The 21-year-old, whose father Vladimir Weiss Snr is the coach of the Slovakia national team, played a prominent role in City's pre-season tour of North America but has been told by Citizens boss Roberto Mancini that his first team opportunities this season will be limited.
City have already sold a number of their fringe players this summer, including Shay Given and Jerome Boateng.
Source: Team Talk
Source: Team Talk