The 55-year-old Duke of York tweeted a picture of himself wearing the watch at a meeting of the Commonwealth veterans' group.
Andrew is believed to have received the expensive gadget as a gift, the Independent reported.
He received more than 100 gifts last year during official engagements, including a model surface-to-air missile.
"A list of gifts received will be released in the usual way in early 2016," Andrew's spokesman was quoted as saying by the newspaper.