The glass sphere that Christ holds in one hand may well prove the clinching evidence that a recently cleaned painting is a newly discovered work by none other than Leonardo da Vinci.

Leonardo had many imitators in 16th century Milan but their efforts are miserably below his standard. Looking at the newly cleaned Salvator Mundi, which will be exhibited at the National Gallery this autumn as a rediscovered work by Leonardo, the transparent orb is far too brilliantly painted to be the work of one of his disciples.

Leonardo was obsessed with problems like how to create translucent effects in painting, how to capture the mysteries of light – the very problems posed by painting a glass sphere.

Such genuinely Leonardesque touches have turned an unloved painting sold for £45 in 1956 into what is now claimed to be a Leonardo worth £120m. The painting, acquired in 2005 by a consortium of businessmen, was recently restored. It was then shown to Nicholas Penny, director of the National Gallery and Luke Syson, curator of its forthcoming Leonardo exhibition. The exhibition catalogue and captions will say it is "by Leonardo da Vinci" – which is about the most spectacular claim you can make for any old painting.

The number of lost Leonardo works almost equals his known paintings. Leda and the Swan, a provocative nude, was probably destroyed by a shocked religious member of the French royal family. The Battle of Anghiari was covered or destroyed at the behest of the Medici. A nude Mona Lisa, the Mona Vanna, is another lost work. Salvator Mundi, is described in 17th century documents but long thought to have vanished.

He gazes softly, wisely, from falling curly locks – another Leonardo trait is a love of ringlets and spirals – and raises his right hand in benediction. The complicated design on his tunic resembles a drawing in the Royal Library, Windsor, apparently a study for this painting, that will also be shown in the exhibition. This work is clearly connected with The Last Supper: the Christ has the same ethereal and elusive quality as the faded figure at the centre of Leonardo's sublime mural.

The glassy orb, an image of the world or the cosmos, makes you think of Leonardo's scientific research and his philosophy of the microcosm of the human being within the macrocosm of the universe. The National Gallery believes its exhibition will be the perfect place to test this painting against his established works. One of the most exciting things about the discovery is the light it may cast on Britain's relationship with Leonardo – for this painting once belonged to Charles I. Later in the 17th century the royal family got its hands on the best collection of Leonardo drawings in the world.

If Charles I owned a real Leonardo before he was executed in 1649, this means our national love affair with the Renaissance polymath has been going on for almost 400 years.