Smith, who was on his way to meet fellow tea importer TG Matthews in Brooklyn, New York, was among the 1,500 who died in the disaster, although his body was never identified.
Its buyer was the Titanic Museum Attraction in Pigeon Forge, Tennessee, and Branson, Missouri, and the seat is to go on exhibition, the auctioneer said.
The auction comes as Southampton marked the 114th anniversary of the RMS Titanic tragedy at a memorial on 14 April.