The Daily Telegraph reported Thursday a meeting of union members gave tentative approval to the agreement, which now will be put to a vote among BASSA's 10,500 members.
The newspaper said the tone of the talks improved when BA's Chief Executive Officer Willie Walsh was replaced with Keith Williams.
At the union meeting, members cheered loudly when they heard Walsh had stepped down.
The dispute between the union and the airline began with disagreements over schedules imposed during the economic downturn. Union members later dug in their heels in protest of disciplinary action the airline imposed on some members who took part in early walkouts.
In total, union members walked off their jobs for 22 separate work stoppages. The disruptions cost the airline about $244 million, the Telegraph said.
The union is expected to vote on the new agreement by June.