Passengers will be able to connect to a 4G broadband network, giving them “the internet access they expect on the ground while in the air”, IAG said.
The work will start next summer at BA’s engineering base at Glasgow airport, where it maintains its short-haul fleet.
The company’s other airlines - Aer Lingus, Iberia and Vueling - will also provide the service.
Willie Walsh, IAG chief executive, said: “We are giving our customers the fastest connectivity you can get on any aircraft.
“Having announced wi-fi for long-haul flights earlier this year we are now equipping our airlines’ short-haul fleets with inflight broadband access.
“Connectivity is essential because it’s what our customers demand and IAG will be the first European airline group to offer high quality air to ground wi-fi on short-haul flights.”
IAG’s first short-haul aircraft equipped with wi-fi will be a British Airways A321, with the service launched next summer. Aer Lingus, Iberia and Vueling aircraft will follow later in 2017.
By 2019, 90% of IAG airlines’ fleets will be fitted with wi-fi.