Evans was due to face Brabners in the High Court in London this month, in a bid to recoup loss of earnings, claiming he was badly advised by them.
However, it is understood that the Welsh striker will no longer be pursuing the case with reports in national media outlets stating Evans had accepted an out-of-court settlement from the law firm.
The 30-year-old was the top scorer for Sheffield United and earning around £20,000 a week when he was originally convicted of raping a 19-year-old woman in a hotel room in North Wales in 2011.
In court he was represented by Matthew Bennett and former Blackburn Rovers winger Stuart Ripley, both of Brabners, and was subsequently released by the Blades.
After serving half of a five-year sentence, Evans was later freed and vowed to fight to clear his name.
A retrial was then ordered in 2016 after the Court of Appeal quashed his conviction and, at a second trial at Cardiff Crown Court, a not guilty verdict was reached by the jury who took less than three hours to come to a conclusion.
Following his release Evans was in talks with Oldham, however the move fell through following outrage from sections of the public.
He later signed for Chesterfield and subsequently moved back to Sheffield United for £500,000 in 2017 before joining Fleetwood on loan.
So far this season he has scored 16 goals for the League One side, including a brace in a 2-2 draw with Southend United on Saturday.
A spokesperson for Brabners said: “We are glad that Ched Evans has agreed not to pursue this case, which we believe was entirely without merit.
“Brabners put forward a strong defence of Mr Evans claim following a thorough process and we were prepared to vigorously defend our handling of the case.”