Current as of AL Player's Guide v11.0.
The Adventurers League Player's Guide covers what is a legal DDAL resource. From the AL Player's Guide v11.0:
You can use non-optional rules found in the Player’s Handbook,
the Basic Rules, and all the books listed below.
Eligible sourcebooks containing backgrounds:
Official D&D Adventure Products
- Hoard of the Dragon Queen
- Rise of Tiamat
- Out of the Abyss
- Curse of Strahd
- Tomb of Annihilation
- Ghosts of Saltmarsh
- Baldur's Gate: Descent into Avernus
- Icewind Dale: Rime of the Frostmaiden
- The Wild Beyond the Witchlight
D&D Adventurer's League and Guild Adept Products
- Ruins of Mezro
- Rats of Waterdeep
- Durnan's Guide to Tavernkeeping
- Knuckleheads and Other Curiosities
Premier Organizer Products
- The Border Kingdoms
- Moonshae Isles Regional Guide
Official Backgrounds from Sourcebooks
- Acolyte (BR, PHB)
- Charlatan (PHB)
- Criminal (BR, PHB)
- Criminal Variant: Spy (BR, PHB)
- Entertainer (PHB)
- Entertainer Variant: Gladiator (PHB)
- Folk Hero (BR, PHB)
- Guild Artisan (PHB)
- Guild Artisan Variant: Guild Merchant (PHB)
- Hermit (PHB)
- Noble (BR, PHB)
- Noble Variant: Knight (PHB)
- Outlander (PHB)
- Sage (BR, PHB)
- Sailor (PHB)
- Sailor Variant: Pirate (PHB)
- Soldier (BR, PHB)
- Urchin (PHB)
- City Watch (SCAG)
- Clan Crafter (SCAG)
- Cloistered Scholar (SCAG)
- Courtier (SCAG)
- Faction Agent
- Far Traveler (SCAG)
- Inheritor (SCAG)
- Knight of the Order (SCAG)
- Mercenary Veteran (SCAG)
- Urban Bounty Hunter (SCAG)
- Uthgardt Tribe Member (SCAG)
- Waterdhavian Noble (SCAG)
Also worth noting is that D&D Adventurer's League supports customizing a background, as per the PHB rules for doing so. While this allows for a custom selection of skill proficiency and tool/language proficiency, you're still restricted to equipment packages and background features as published.
Backgrounds from D&D adventures and other products
- Cult of the Dragon Infiltrator (HotDQ, RoT)
- Dragon Scholar (HotDQ, RoT)
- Deep Delver (OotA)
- Underdark Experience (OotA)
- Haunted One (CoS)
- Anthropologist (ToA)
- Archaeologist (ToA)
- Fisher (GoS)
- Marine (GoS)
- Shipwright (GoS)
- Smuggler (GoS)
- Faceless (BGDiA)
- Feylost (TWBtW)
- Witchlight Hand (TWBtW)
- Heretic (Ruins of Mezro)
- Detective (Rats of Waterdeep)
- Tavern Worker (Durnan's Guide to Tavernkeeping)
- Tavern Regular (Durnan's Guide to Tavernkeeping)
- Arctic Guide (Knuckleheads)
- Cold Water Fisherfolk (Knuckleheads)
- Goliath Seeker (Knuckleheads)
- Prospector (Knuckleheads)
- Skald (Knuckleheads)
- Survivor (Knuckleheads)
- Whaler (Knuckleheads)
In addition, Baldur's Gate: Descent into Avernus contains alternate features for all 13 of the PHB backgrounds.
Additional Material
MOONSHAE ISLES & BORDER KINGDOM CHARACTERS
If you’re participating in adventures set in either of these locations,
you can use their respective products (found on the DMs Guild) to
select a background for your character.
Rising Shadows-Moonshae Isles Regional Guide
The Border Kingdoms: A Forgotten Realms Campaign Supplement
The information for older editions can be found here: