The painting is considered special as it was “exceptionally rare” for a non-white veteran of Waterloo to appear in a portrait in 19th-century art, the museum says.
Having acquired the artwork earlier this year, trustees of the Chelsea museum wanted to uncover the story behind it.
The sitter had to be one of only nine black soldiers known to have been awarded the Waterloo Medal, as seen in the portrait, the museum’s art curator Anna Lavelle said.
Researchers narrowed the list of candidates down further from other items in the painting.
“Those items were placed there for a reason – they tell a story,” Ms Lavelle said.
The solider wears a fur pelisse and holds a cymbal, which meant he was very likely to have belonged to a cavalry regiment, Ms Lavelle said.