Philippa Langley finished a screenplay about the medieval monarch's life last year, months after she led archaeologists to a spot where a skeleton believed to be his was found.
Ms Langley, 50, who is secretary of the Scottish branch of the Richard III Society, came up with the idea of the search during a meeting of the group in February 2009.
Results of tests are to be revealed over the next day or so, conclusively proving whether the remains are indeed those of the last Plantagenet monarch.
Ms Langley contacted Armitage, 41, who plays dwarf leader Thorin Oakenshield in Peter Jackson's blockbuster, and says he agreed to take on the role. Armitage has also starred in a number of television series including Spooks, Robin Hood and the Vicar of Dibley.
Richard III was killed at the Battle of Bosworth in 1485 by the forces of Henry Tudor, effectively ending the 30-year-long War of the Roses.
He is often regarded as an ugly, hunchbacked tyrant, but Langley believes history has judged him unfairly and the popular view of him stems from the Tudors, who were keen to damage his reputation in order to justify his killing.
Her screenplay presents a sympathetic portrait of him, underlining his accomplishments such as the introduction of the presumption of innocence of an accused facing trial.
It also disputes the opinion he was responsible for the murders of his nephews, 12-year-old Edward V and nine-year-old Richard, Duke of York, the so-called Princes in the Tower.
"I had to write the screenplay. Richard III's story has to be out there. I want that story to be told. I had Richard Armitage in mind to play him and he has agreed," said Ms Langley.
"Not only he is a dead ringer for Richard III, but he was born a few miles away from Bosworth field and was named after him."
Ms Langley, who lives in Edinburgh, is now seeking funding for the film.
She has also drawn up plans to give the dead monarch a proper burial, commissioning an artist and historian to design a tomb if, as expected, tests confirm the remains found in a car park in Leicester in August are his.
A photograph given exclusively to The Herald shows part of the tomb. It is decorated with the White Rose, the heraldic sign of Richard's House of York, and the cross of St Cuthbert, one of his most venerated saints.
"I always had two aims," said Ms Langley. "One was to undertake original research into Richard III and to bring the real historical figure to the forefront rather than the Shakespearean and Tudor version of him.
"But the second, which was actually my main aim, was to try and retrieve his remains from an undignified place and give them the reburial that fits a king."
After Richard III was killed, his body was despoiled before being taken to Leicester, where he was buried in the church of the Franciscan Friary, known as the Grey Friars. However, over time the exact whereabouts of the Grey Friars became lost.
Kirk Wheelan-Foran, Armitage's agent, said: "It is very early days. Richard is not in the country at the moment."
l The documentary Richard III: The King in the Car Park, about Langley's search for Richard III's remains, is to be broadcast on Channel 4 on Monday at 9pm.