Mr Wardrop, a former pupil of Aberdeen Grammar School, had left Scotland during the 19th century to start a new life in Australia.
The postcard was sent from Queensland in 1889 but only reached its Scottish destination two days ago.
The Royal Mail launched an immediate appeal for relatives of the intended recipient - a Miss Wardrop of 32 Carden Place, Aberdeen.
The card had been sent to her grandmother by a man named Colin in 1889, but her home is no longer there having been replaced by a dental surgery and three businesses.
Mrs Britts is the granddaughter of Colin Wardrop who sent the postcard to his spinster sister, Minnie.
Mrs Britts said: "I could not believe it when I heard. I will be so pleased to get the card."
The card only left Australia earlier this month, despite being posted on 4 January, 1889.
Mr Wardrop, a former pupil of Aberdeen Grammar School, had left Scotland during the 19th century to start a new life in Australia.
He eventually became head of the National Bank of Queensland in Brisbane.
Now the postcard will be sent back to Australia to become a family heirloom for Mrs Britts.
Royal Mail's area manager for Aberdeen, Peter Smith, said: "We will now go the extra 12,000 miles to ensure this very important postcard reaches its rightful destination."
The postcard will be sent to Australia next Monday and should arrive within four working days.
The card has an elaborate crest in its top left corner and was posted with a threepenny stamp.
The message reads: "Just a few lines to say that I am still in Brisbane and have enjoyed my six weeks' leave.
"I reported myself today at the bank, but have not yet heard my destination. Thanks awfully for letters from you and Gerty.
"Trusting you are all well and wishing you all a happy new year. Will write in a day or two. This is the first time postcards have been issued in Queensland."