Delta Air Lines is close to an agreement to merge with rival Northwest Airlines in a tie-up that will create the world’s largest carrier and help insulate the combined company from a bitter industrywide downturn.

The accord, which is set to be announced on Tuesday but could be confirmed as early as Monday, will cap several months of negotiations between each airline and their pilots, people familiar with the matter said. The stand-off by the pilots in finding common ground on how to rank their members by seniority threatened to scuttle the merger last month.