Heathrow Airport says BA now expects to run a full flight schedule today.
But BA says there is still work to do to reunite a "significant number of passengers" with their missing luggage.
The company's boss Alex Cruz told media outlets the power outage which caused the disruption was "a tragedy".
He denied claims from the GMB union the problems were down to BA cutting "hundreds of dedicated and loyal" IT staff and contracting the work out to India to save money.
Mr Cruz insisted those parties involved in the weekend's problems had "not been involved with any type of outsourcing in any foreign countries".
"They've all been local issues around a local data centre who have been managed and fixed by local resources," he said.
Mr Cruz said there was "no evidence whatsoever" a cyberattack was behind the computer problems.
He instead cited a "power surge" at around 9.30am on Saturday morning for the "catastrophic effect" on all of BA's systems.
Later today Comms Business anticipates a flood of channel advice for BA to pour in regarding the defective set up and testing of business continuity options.
We'll keep you posted.