Paul Clark, his wife Jiorgia and their four children travelled to London from Washington state, in the US, on holiday.
The family saw firefighters battling the blaze while they were on the London Eye on Saturday.
“It was sad to see,” Mr Clark told the BBC.
He said they were all worried the artwork had been damaged but were “very relieved” to hear it was safe.
Mr Clark said he is a huge fan of Vincent Van Gogh. The gallery houses the painter’s famed Self-Portrait with Bandaged Ear.
A fire broke out in the west wing of the building, which is mostly used for offices and storage, at about midday on Saturday.
The director of Somerset House Trust, Jonathan Reekie, said there were “no valuable artefacts or artworks” in that part of the building.
The day after the blaze, multiple fire engines were still parked outside.