The discovery "is a real detective novel of a story," said its restorer Paolo Cherchi Usai, who also helps organise a silent film festival in northeast Italy where the showing is taking place.
"Too Much Johnson" (1938) is believed to be the first professional film by Welles and was intended to be shown as part of a play, as the theatre director was making his transition to film-making.
Cherchi Usai said the last known screening of the film was in the 1960s and the reels lay undiscovered in storage in Italy for 30 years.
"It is a real mystery. I only have a few facts," Cherchi Usai said.
Welles worked for many years in Italy and Spain.
"The reels were in surprisingly good shape even though they were not kept in the right conditions, except for one where you could not see a thing which was restored in the Netherlands," he said.
Film expert Cherchi Usai carried out most of the restoration himself at the George Eastman House film institute in Rochester in the US state of New York, where the original is now being stored.
The festival is being organised in Pordenone, the same Italian city where the film was found.
The short film - a slapstick comedy - is considered his first professional film work and shows early signs of the director's signature style of shooting his subjects from below pointing up, giving them a statuesque, monumental quality.
Cherchi Usai said film buffs and journalists from around the world are coming to the showing on Wednesday, which will be followed by a screening in the United States later in the month.
"We have been inundated with requests and the showing has been booked out for months. We have been forced to organise two more showings on Friday to accommodate all the requests," he said.
Best known for the 1941 classic "Citizen Kane" and, in 1938, the science fiction radio drama "The War of the Worlds," Welles was a co-founder of the Mercury Theatre. He died in Los Angeles in 1985 at the age of 70.