The National Gallery in London announced on Thursday that it had secured funding to purchase Titian’s “Diana and Callisto” together with the National Galleries of Scotland for $71.7 million, thereby ensuring that the work, along with another great painting by the 16th-century master, would stay on public view.

“Diana and Callisto’’ belonged to the Duke of Sutherland, who sold another Titian, “Diana and Actaeon” to the two museums for $71 million in 2009. At the time, the Duke gave the institutions the option of purchasing the second painting for about the same price. They were also given 2012 as a deadline....