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His previous club Norwich will receive 20% of the fee.
It had earlier been reported in the media that United would have to wait a little longer to hear the worth of striker, but that is now not the case.
A group led by chairman Steve Wharton and vice-chairman Rex Garton went to Preston to put forward their case to the FA committee.
Hayes finished as United's top scorer last year, but opted to move to League One rivals Barnsley when his contract expired in the summer.
This brings an end to a saga that has gone on for three months, Hayes actually joined the Reds on June 2.
The two club's had failed to agree a fee, with United rumoured to have turned down Barnsley's original offers more than once.
He has since scored twice for Barnsley - scoring in their 2-0 opening day win over Swindon, and also netting in their 2-1 defeat at Glanford Park in August.
Iron boss Brian Laws earlier said: "I'm hoping that we get the money that we deserve, he's a good player - he scored 20 goals last season.
"He's a striker with calibre and ability, and we wanted to keep him. Barnsley have got an excellent player on their hands and we hope they don't get him cheaply."
The FA decided earlier today that Preston must pay Port Vale a fee of up to £105,000 for striker Dave Hibbert.
He joined North End from Vale in the summer but despite the player being out of contract, the League One club were due compensation as Hibbert was under the age of 24.
With the clubs unable to agree a fee, a Manchester transfer tribunal has ruled the Deepdale club should pay an initial £85,000 for the 20-year-old, with a further £20,000 if Preston are promoted, as well as a sell-on clause.
It also ruled that League Two side Bury could receive a total of £100,000 from Oldham for striker Chris Porter.
He was out of contract at Gigg Lane in the summer but the 21-year-old was not allowed a Bosman free transfer as he is under the age of 24.
Shakers director Ian Harrop felt the transfer tribunal in Manchester judged in Bury's favour and was satisfied with the ruling, which will see the League Two club awarded £50,000 up front, £25,000 after 15 appearances and a further £25,000 after 30 appearances, as well as a 15% sell-on clause.