Barcelona-based Level will initially use two new Airbus A330 aircraft to serve the Americas, with fares starting from Â£99 one-way.
Its first flight from Barcelona to Los Angeles takes off on Thursday.
It will be followed by flights to San Francisco, Buenos Aires and the Dominican Republic in the coming weeks.
Tickets have been on sale since March and IAG said it sold 100,000 in the first month.
BA has been at the centre of controversy following a disastrous computer crash that stranded 75,000 passengers over the weekend.
Critics have said that BA has been relentlessly cutting costs to take on competition from budget airlines. BA denies that this caused the IT problems which it blames on an electrical power surge.
But IAG Group, which also owns Aer Lingus and Vueling, is now pinning its hopes on the new airline to help it compete in an increasingly aggressive trans-Atlantic market.
Level's pricing structure is divided into six types of fare. The most basic includes hand luggage only.
The most expensive is flexible premium economy which offers a hot meal, two checked bags, and seat selection. Wifi is available with prices starting at 8.99 euros.
It will start out with flight and cabin crew from its sister airline Iberia and will create up to 250 jobs based in Barcelona.
IAG chief executive Willie Walsh, said: "This is just the start. In summer 2018 we will have more aircraft and will operate more destinations from Barcelona. We're also planning to expand Level operations to other European cities."
The competition has ratcheted up since the arrival of the Boeing 787 Dreamliner in late 2011. The plane, made from composite materials was lighter, more fuel efficient and cheaper to fly than any of its predecessors. Aerospace analysts considered it a game changer for the airline industry.
The Oslo-based budget airline Norwegian jumped at the opportunities the new aircraft offered.  It now has 13 Dreamliners in service with 30 more on order to fly passengers from cities including London and Paris across the Atlantic.
This year Norwegian started offering one-way fares starting at $65 between smaller airports in the UK and Ireland to similar destinations in New York state, Providence, Rhode Island, and Hartford, Connecticut.
Level has taken a different tack, opting for the latest version of the Airbus A330, which is intended to take on the Dreamliner, and is fitted with 293 economy and 21 premium economy seats.
But the trans-Atlantic budget air space is about to get very crowded.
From July Iceland's budget airline WOW will be offering flights from London Gatwick, Bristol and Edinburgh to Chicago from Â£139, and Lufthansa's Eurowings subsidiary will be increasing its low cost offerings to Orlando, Florida and Seattle.
The owner of British Airways, IAG, said its new trans-Atlantic budget airline will expand its fleet to five planes and aims to open new European bases.