if anyone knows the answer to your question, it will be Rory Muir who visits this site occasionally. From memory, I do not believe Arthur Wellesley's reading list survives.
Instead, I can tell you what Major Edward Cocks had sent out to him prior to his death on campaign in 1812. This is more relevant than you might think, since Cocks was a particular favourite of Wellington's and was being groomed by him for higher things. I shall confine myself to the military titles:
de Saxe, Reveries
Essai Generale de Fortification
Jomini, Traite de la Grand Tactique
Memoirs of Prince Eugene
Lloyd, History of the Seven Years War
Bouchon, Treatise de la Guerre de la Vendee
Beaurzan, Histoire de Cartes dernier compagnie de M. de Turenne
In one letter home, Cocks asks for a new translation of the 1792 French regulations and for 'anything by Egerton'. The last named was a publisher who started a series called 'Egerton's Military Library'. The heyday of this imprint was 1804-1810 and broadly it coincided with the period when the Brits realised they had to do something to brush up on the woeful professional education of their officers. Indeed, the Duke of York, Commander in Chief, seems to have patronised Egerton's venture in order to boulster it. The Military Library series includes many different fascinating texts on the latest military theories, including translations of foreign works.