Sir Stanley signed for his home team of Stoke City in 1932 and was knighted while still playing professionally.
As well as £5 a week in wages, he was offered a £10 signing-on fee "plus the usual bonus" - a princely sum for a player at the time.
The family behind the sale hope the British Football Museum will purchase the piece of sporting history.
Brothers David, 53, Andy, 56, and Graham Lockett, 61, who live in Stoke and support the club, are also selling a second Sir Stanley contract, dated 1935.
Their father Les took ownership of them in exchange for a debt and were discovered by his sons while they were having a "a clear out" after his death.
"That's the way business was done back in the 60s. A bit like a pawn shop," David said.
"The contracts have been gathering dust in a drawer for nearly 50 years."
Sir Stanley's wages rose in 1935 to £7 - £8 if he made it into the first team - which equated to about £350 a year.
The family said it was important for people to know what top players earned in the 1930s.
"Compared to what they earn today, it may seem ridiculous but at the time it would have been a lot of money," David added.
Sir Stanley, born in Hanley on 1 February 1915, played almost 700 games for Stoke and Blackpool and gained 54 England caps before retiring in 1965, aged 50.
He died in 2000, aged 85.
Sir Stanley, who was knighted in 1965, was described by then-Prime Minister Harold Wilson, as "a symbol of the country which gave football to the world, and internationally a symbol of English sportsmanship in the days when that was a quality acknowledged worldwide".
The contracts go under the hammer with Hansons Auctioneers on 22 August with a guide price of between £1,000 to £2,000 for the 1932 contract and £500 to £800 for the 1935 document.
The first professional contract signed by footballing legend Sir Stanley Matthews is to go on sale at auction.