The picture, of a young, bearded man wearing a Roman-style laurel crown and holding an ear of sweetcorn , was identified by botanist and historian Mark Griffiths and will be published in Country Life on Wednesday.
Until now, the only accepted authentic likenesses of Shakespeare, in which he is depicted as bald, have been found in the First Folio of his works and his monument at Holy Trinity Church, Stratford-upon-Avon, both created posthumously.
Speaking on the magazine website, Griffiths said the discovery had come when he began researching the biography of pioneering botanist John Gerard (1545-1612), author of The Herball or Generall Historie of Plantes, published in 1598.
"I began to look at the title page engravings ... and realised it was full of allusions to people who had been involved in the creation of the book and that four of the figures on the title page were in fact real persons," he said.
Three were Gerard himself, Flemish botanist Rembert Dodoens and Queen Elizabeth's Lord Treasurer, Lord Burghley, Griffiths said. The plants and motifs surrounding them in the engraving appeared to be elaborate Tudor references to the men themselves.
"And then there was a fourth figure who was dressed as a Roman and appeared to have something to do with poetry," he added.
Griffiths also discovered a cipher underneath the cover image containing clues about the fourth man.
"As I worked hard on this fourth figure, I realised it had to be William Shakespeare," he said.
Griffiths believes that in the engraving the Shakespeare figure is aged 33 and at the height of his celebrity – after writing "A Midsummer Night’s Dream" and shortly before "Hamlet."
He believes Shakespeare was given his literary start by Burghley and that he became almost a propagandist for him.
Previous claims of discoveries of portraits of Shakespeare created during his lifetime have been generally disbelieved by scholars.
But Country Life editor Mark Hedges was in no doubt. He said in a statement: "We have a new portrait of Shakespeare, the first ever that is identified as him by the artist and made in his lifetime."