Veteran boss Brown and his assistant Knox, both now at Aberdeen, launched a legal action against the Fir Park club in May.
They reportedly believed they were each owed ?12,500 for helping Motherwell reach the Co-operative Insurance Cup semi-finals and the third qualifying round of the Europa League.
In a statement, Motherwell chief executive Leeann Dempster said: "Having strongly defended our club's interests over two separate tribunal hearings, we welcome the news that the claims have been withdrawn and a line can now be drawn under that short chapter.
"Motherwell's whole focus as a club is on building a long-term sustainable future and successful team bringing enjoyment and benefits to our fans and our community."
Source: Team Talk
Source: Team Talk