It was Claude Lorrain who reduced J. M. W. Turner to tears. Not the man himself, who died almost a century before Turner’s birth, but one of his paintings, which belonged to banker-collector John Julius Angerstein. In response to Angerstein’s enquiry into the cause of Turner’s tears, the latter reportedly exclaimed: ‘Because I shall never be able to paint anything like that picture.’

But within a matter of years, Turner had proved himself wrong. Included in an exhibition opening this week at the National Galleries of Scotland is a heroic Claude-inspired landscape complete with Classical ruins, limpid pools, white-gold sunlight and a craggy horizon. In Lake Avernus: Aeneas and the Cumaean Sibyl, of 1814–15, the partly self-taught barber’s son from Covent Garden paid homage to the earlier master in a vision of sweeping grandeur irradiated with the warmth and drama of the untamed south.

The exhibition ‘Turner and Italy’ is a visual souvenir of a love story. Turner had most likely fallen in love with Italy before his first visit in 1802, at the age of 27. A child prodigy, he was accepted as a student at the Royal Academy Schools when he was only 14. There he encountered works by Canaletto, Richard Wilson, De Loutherbourg and John Robert Cozens, in addition to the paintings of Lorrain. These artists were beguiled by and, in turn, beguiled others with their depictions of a country remote from the dark scars of Britain’s emergent Industrial Revolution embraced by the sun and coloured by the majesty of a Classical past still celebrated throughout the civilised world.

This was the country Turner discovered for himself in 1802, and to which he would return on six further occasions. His visit to Rome in 1819 also took in Turin, Milan, Venice, the Lakes, Bologna, Ancona, Spoleto, Narni, Naples, Sorrento, Amalfi, Paestum and Florence. Although he would afterwards describe Rome as the ‘Land of all Bliss’ and made protracted stays in Venice, his enthusiasm for Italy as his sketchbooks show embraced the whole country.

The experience of Italy didn’t revolutionise Turner’s art. Rather, it imbued his work with that ‘Grand Manner’ so valued by Reynolds, whose influence dominated the Academy Schools throughout Turner’s studenthood. It also awakened in Turner insights into the transforming power of light and colour, which would afterwards play central roles in his development both as artist-practitioner and Romantic visionary. The relationship of light and colour, as much as topography or architecture, is the concern of paintings such as Florence from San Miniato of 1827 and Modern Rome Campo Vaccino (1839).

Perhaps these were included among the paintings seen in Turner’s house by Lady Trevelyan the year after the artist’s death: ‘Among bits of furniture thick with dust… brilliant pictures all glowing with sunshine and colour.’ Her description would equally have applied to Approach to Venice, a sun-drenched meditation in which land and lagoon are bathed in the same diamantine light. In all three paintings, that light is the glow of a great artist’s enduring affection for the country that inspired him.

‘Turner and Italy’ is at the National Galleries of Scotland, Edinburgh, from March 27 until June 7 (0131–624 6200; www.nationalgalleries.org)