The Premier League club have agreed to pay Atletico Nacional a deal totalling €10 million for the 19-year-old.
City believe they have beaten off rival interest from Manchester United and Benfica in the race for the speedy winger, who was also linked to Liverpool, although personal terms are yet to be finalised.
Moreno is unlikely to get a work permit in the interim, and the Blues are keen to send him out on loan, most likely to Spain, for the 2016-17 season.
His rise in South America so far has been impressive. The Medellin-born forward made his debut for Atletico as a 17-year-old in 2014, and helped seal the destination of the 2015 league title when he scored the fastest goal in the club's history in the deciding match.
READ MORE | Nolito: No contact with Barca or Man City
After just a handful of appearances for Colombia's Under-17 side he was fast-tracked to the senior team in March, and was quickly called up to Jose Pekerman's squad for this summer's Copa America, where he scored his first international goal against Costa Rica in the group stages.
That game against the Central American side was his only start at the tournament, but he was brought on at half-time of Colombia's semi-final defeat to Chile in a bid to overturn a 2-0 deficit and played a role in the third-place play-off.
City have been watching Moreno's performances closely throughout the tournament and have been sufficiently impressed to step up their interest and close out a deal.