The two models will make their world premiere at the 2015 Geneva show in March and go on sale shortly after.
Opel's version is named after one of the company founder's sons, while the UK version revives Vauxhall's Viva name for the first time since the original ended production in 1979.
North America and possibly other markets as well, will get GM's new city car in the form of the next generation Chevrolet Spark with a modified appearance.
The Karl and Viva are positioned at the bottom of Opel and Vauxhall's passenger car range, below the Adam, and are expected to start under €10,000 in Europe , which would position them against the Fiat Panda, Kia Picanto, Hyundai i10 and VW Up!.
GM's new mini is 3,680mm (144.9 in) long, making it slightly shorter than the Adam (3,700mm) and a lot smaller than the new Corsa (4,000mm), though the automaker claims that it offers enough room for five passengers.
It's expected to weigh about 900 kg (1,984 lbs) with power coming exclusively from a newly developed 1.0-liter three-cylinder petrol engine delivering 75PS (74hp).