The SPL club had refused to accept the right of the Scottish Football League to decide compensation, and Ayr say they will now contact the Scottish FA to seek revised rules for resolving such disputes in the future.
Conway has made 30 appearances for Dundee United since moving from Somerset Park in the summer.
Ayr United said in a statement on their website: "Agreement was reached based on a guaranteed fee 60% higher than the guaranteed fee offered by Dundee United at the time of their signing the player.
"In addition, a 20% sell on clause was also agreed. 10% sell-on had originally been offered.
"Craig's good form and regular appearances earlier in the season succeeded earlier this year in transforming into guaranteed fee that part of the fee which was offered conditional upon appearances."
Ayr had initially demanded £180,00 based on world governing body FIFA's compensation rules. Unfortunately this ruling does not apply to domestic transfers.
"The level of compensation payable should not be substantially lower simply because the player had moved to a club within the same country," they stated.
"Unfortunately for Ayr United, there appeared to be weaknesses within both the wording of the SFL and SFA rules on compensation disputes between SFL and SPL clubs and these were a concern.
"It was against this background of probable continued dispute that Ayr United decided to settle.
"The terms agreed by Ayr United reflect the fact that our negotiating strength was impaired by the apparent weaknesses in the rules and vice-chairman Mark Meehan will meet with the SFA's in-house lawyer to assess the difficulties encountered with a view to revised rules being proposed among SFA, SFL and SPL .
"Entitlement to compensation for players under 23 is a fundamental principle embraced by FIFA.
"Ayr United intend fully exploring every aspect of the Craig Conway compensation dispute to ensure that our rights have been properly accommodated."
Despite the constraints Ayr United should be congratulated on challenging the bullying tactics of the SPL club and obtaining a settlement more befiting the calibre of the player.