Britian's leading public art centres have reached an agreement after a row broke out over the National Gallery's plans for a Picasso exhibition, set to open next week.

Next week, the National Gallery in Trafalgar Square opens an exhibition devoted to the work of the Spanish titan of 20th-century art, Picasso (above Reclining Nude, 1969 by Picasso)

Defining any period of history is a tricky business, but when it comes to art history, fixing the dates of movements and styles can be especially contentious – with important financial ramifications for museums and galleries.

Next week, the National Gallery in Trafalgar Square opens an exhibition devoted to the work of the Spanish titan of 20th-century art, Picasso. The show is likely to be the hottest ticket in the art world this spring, bringing in substantial revenue for the museum's coffers.

And yet, according to the terms of an agreement thrashed out in 1996, the exhibition encroaches on the territory of the Tate. At that meeting, the heads of both institutions agreed upon a dividing line between the collections. The National Gallery bound itself to not show any art made after 1900, leaving Tate free to cover international art made from the start of the 20th century to the present day.

However, the agreement lapsed in 2007, leaving the NG free to mount shows of modern and contemporary art, hence its decision to bring the touring blockbuster exhibition, Picasso: Challenging the Past, to this country. Tate's director, Sir Nicholas Serota, might be forgiven for feeling piqued by his rival's decision to put on a big Picasso show – after all, in 2002, Tate Modern hosted an important exhibition devoted to those two giants of modern art, Matisse and Picasso.

Last year, however, the new director of the National Gallery, Nicholas Penny, was unrepentant. "The idea is not to have an agreement," he reportedly said in September. "We are not happy with 1900 as a final, absolute point of the end of the National Gallery." You can understand his concern, of course: these days, modern art is big business. And, from a scholarly viewpoint, limiting what you can show to an arbitrary date is highly reductive. Art historians could argue for aeons about the exact year in which Modernism started – and for many of them, 1900 wouldn't be their first choice.

So where does that leave things today? Yesterday, it was announced that a new agreement lasting until 2019 has been reached, reportedly to the satisfaction of both parties. "Following recent discussions, the National Gallery and Tate have agreed that the principles governing the historical boundaries of their two collections, which were put in place in 1996, should continue to apply for another 10 years from 2009," a statement read.

The key point, though, is that the new agreement will have a greater degree of flexibility than the old one: the NG accepts that Tate will continue to acquire 19th-century paintings by artists associated with the 20th century (such as Bonnard and Matisse), and vice versa. "It's a harmonious working out of how we're going to do things from now on," says Thomas Almeroth-Williams of the National Gallery.