The payment has averted the prospect of a court battle over the debt, after Murdoch last week instructed lawyers to sue Desmond's Northern & Shell over its aggressive treatment of her firm, Shine Productions.
Murdoch accused Northern & Shell of "throwing its weight around" and also pledged to assist any other independent producers who had not been paid by Channel Five.
In response, N&S claimed that it had already made contractual payments of more than £5 million for the music talent show, which was fronted by former Spice Girl Emma Bunton.
The company further said that the payment delay was merely because it was querying the details of a final invoice, believed to be for just less than £1m.
Shine, which produces a number of shows for Channel Five including The Wright Stuff, has confirmed that the payment has now been received, bringing to an end the threat of legal action.
In a statement, a Shine spokesperson said: "Shine Group can confirm that payment of all remaining instalments for Don't Stop Believing have now been received.
"This follows Shine readily facilitating further reviews of the programme's accounts for Channel Five after which it was confirmed that no outstanding questions remain. As such, planned legal action to recoup these payments does not need to be pursued."