The rare three-volume set was expected to sell for between £50,000 and £70,000.
The sale, at Bonhams in London, set a new world record auction price for a printed book by the novelist.
The work, inscribed on behalf of Austen to her friend and governess Anne Sharp, was bought by a telephone bidder.
The anonymous British vendor of the book said: “The family are delighted with the price fetched today. The novel had been sitting in my family library for at least three generations.”
The seller is descended from a family that married into the family of Richard Withers, who was left the property of Sharp when she died.
Austen’s publisher was asked by the author to send out 12 presentation copies to friends and family.
The copy was the last on Austen’s list and was sent to Sharp, who had initially been governess to the children of Austen’s brother Edward, and remained her good friend.
Austen created the governess character of Miss Taylor in her novel Emma.
The story was first published in 1816 and follows the perils of misconstrued romance in Regency England centring around Emma Woodhouse.
In March, Bonhams sold a rare inscribed first edition of JRR Tolkien’s The Hobbit for a world record-breaking £60,000 (€75,000).
In November last year, it sold a rare first edition of Emily Bronte’s dark and powerful love story Wuthering Heights for £114,000 (€144,000).