BBC Wales has learned an agreement has been struck to end the dispute.
It had been claimed a spelling error by officials at Companies House in Cardiff had led to the demise of engineering firm Taylor & Sons.
Companies House records had been amended to show Taylor & Sons had been wound up in 2009.
But the failing business was another firm called Taylor & Son - with "Son" in the singular.
Taylor & Sons dated back to 1875 and more than 250 people lost their jobs when it went under, and former co-owner, Philip Davison-Sebry, claimed Â£8.8m in damages over the mix-up.
In January 2015 the High Court judge ruled in Mr Davison-Sebry's favour and found Companies House, when entering a winding up order, owed reasonable care to ensure the order was not registered against the wrong company.
Companies House began an appeal against the ruling in January last year, arguing the case set a "dangerous precedent".
A full appeal was listed for this month, but BBC Wales has learned an agreement was reached last spring.
A spokesperson for Companies House said: "We have agreed confidential terms of settlement and this case has now concluded."
No further details are being disclosed by either party.
A multi-million pound court battle over a spelling mistake said to have led to the collapse of a Cardiff company has been settled.