The LLC is a registered organization with the Commonwealth of Virginia. There is nothing you would do with a federal agency regarding transferring ownership of the LLC.
You will probably need to see an attorney or use a legal service in order to affect a transfer. The reason for this is that the specific articles of organization of your LLC will determine if and how you would transfer ownership. If you don't have buy-sell provisions in your articles of organization then Virginia law would dictate how the transfer would proceed.
Some sites, such as LegalZoom, talk about how to transfer ownership of an LLC. It may be as simple as creating a bill of sale transferring ownership of the LLC from you to your wife. It may be more complicated based on your operating agreement, if it includes buy-sell provisions, and or Virginia law.
Other web sites talk about how easy it is to transfer ownership. However, they also recommend the use of an attorney.
If you read Virginia law and the Secretary of State's website you will find forms such as the Articles of Amendment for an LLC. An attorney can tell you if all you need to do is amend your operating agreement and then do a bill-of-sale transfer.
Because the transfer is dependent on so many things that are not obvious, e.g. articles of organization, Virginia law, etc., it would be best to seek the advice of an attorney or some other legal service that specializes in LLCs for your locale.