The arrangement between the two airlines will see Stobart Air provide ACMI services on routes to and from London City Airport under the BA CityFlyer brand from November 16.
The deal will require Stobart to recruit 40 new members of staff, 10 captains and first officers and 30 cabin crew, while it will lease two Embraer 190 jet aircraft for three years.
Stobart Air managing director Graeme Buchanan said: "A key part of our growth strategy is to secure additional commercial relationships with airlines.
"This agreement with BA CityFlyer allows us to further diversify the brands we work with.
"Stobart Air is recognised within the industry for its operational excellence and quality of customer service, and this deal demonstrates that we can continue to leverage this reputation to grow our business and secure further commercial relationships."