Known as Sketch to Illustrate the Passions: Senility, it was featured in ATG when Mr Sim bought it at a Bigwoods auction in Stratford in June last year for £31,000.
Mr Sim exhibited it at the Watercolours and Drawings Fair at the Royal Academy in February this year where it won an award for best picture in the fair and generated interest from a number of curators.
Since then, representatives from the Tate, the Louvre and the Getty all viewed the work, but the Met was the first to come up with an offer matching the five-figure asking price.
Mr Sim would not divulge the actual price, but told ATG that although he had made a decent profit, he had refrained from being overly greedy.
"I'm actually pleased for Richard Dadd," he said. "For someone who was incarcerated in Bedlam asylum now to have his work in the world's pre-eminent museum is a great story."
The watercolour itself was part of a series of at least 33 known genre pictures, each depicting a vice, virtue or human characteristic, that Dadd produced during the time he spent in Bedlam after killing his father in 1843. Known as the Passions series, the majority of these images are now housed in national art collections and museums.
Before being consigned to Bigwoods, the sketch had previously been kept in a Nissen hut in the Midlands and, as such, had some minor damp marks at the edges and some surface dirt.
However, it had not suffered from exposure to sunlight, something to which old watercolours are susceptible, and so the colours were particularly well retained.
Mr Sim, who deals privately and through his father's dealership, Michael Sim of Chislehurst, Kent, took it to an English restorer before exhibiting it.
Next month, he is standing at Olympia for the first time where he will offer a previously unknown drawing by the Pre-Raphaelite portraitist Frederick Sandys that had been on the wall of a B&B in Torquay since the 1950s.
