The German car maker also said it would plead guilty to breaking certain US laws.
VW said it was in advanced discussions with the Department of Justice and US Customs about the deal.
The final agreement has yet to be approved by VW's management and supervisory board, which could happen later on Tuesday or Wednesday.
VW said it had negotiated a "concrete draft" of a settlement with US authorities that included criminal and civil fines totalling $4.3bn, as well as appointing an independent monitor for the next three years.
The $4.3bn fine means that the total costs associated with the emissions cheating scandal are set to exceed the $19.2bn the company has set aside to deal with the issue.
VW has already agreed to a $15bn civil settlement with environmental authorities and car owners in the US.