From what I'm reading the moratorium seems to fall under a different term called Presidential Withdraw.
Presidential withdrawal: Under section 12 of the Outer Continental Shelf Lands Act (OCSLA), the President has the power to withdraw certain areas from offshore leasing. This is called a presidential withdrawal, also referred to as an executive withdrawal or presidential moratorium. The past three presidents have used the power of withdrawal to reinforce protection for the areas under the congressional moratorium.
The Congressional Moratorium is the one that gets updated each year it seems.
Congressional moratorium: In the early 1980s, the Minerals Management Service (MMS), the branch of the federal government that manages offshore Outer Continental Shelf (OCS) oil and gas resources attempted to offer virtually all waters around the U.S. to oil and gas companies. There was a loud community outcry from Barrow, Alaska to Key West, Florida. Fishermen nation–wide organized to protect their fishing grounds. Bowhead whale hunters worked to protect areas important for whale migration. Tourist businesses and coastal residents focused on protecting highly vulnerable areas such as coral reefs. As a result, Congress stepped in with the offshore drilling moratorium. Each year since 1982, Congress has passed a measure in the Interior Appropriations bill to prohibit oil and gas leasing or exploration on the Outer Continental Shelf off the vast majority of the nation's coastline.
Both of these come from this link, which gives a good timeline based on Bristol Bay.
History of Protection — Alaska Marine Conservation Council
Let it be said though, the Exxon Valdez spill had nothing to do with offshore drilling. It had everything to do with allowing a known alcohilic to pilot a big boat full of oil. Also, there are a handful of places that are immune to drilling regardless of moratorium, these are Channel Islands and Monterey Bay in California, the Florida Keys, Gray's Reef in Georgia and the Olympic Coast sanctuary in Washington State. Those places are off limits and I don't believe that will ever change. Ironically enough though, Cuba has allowed China and others to explore for oil, and although they've not gone very far off of the Cuban coastline and their exploration hasn't returned any oil yet, they are planning to use slant drilling which when they do hit an oil deposit, it will essentially be a US oil deposit. From the articles that I've been reading over the past hour or so claim that leases off the northern coast of Cuba are still essentially up for grabs, and that China is drilling oil on Cuban land, and exploring for oil on the coasts, but not actually offshore.. yet.