Are there any legendary characters created specifically for Hearthstone?

Solution 1:

Although not a legendary, before The Grand Tournament the only new character was Harth Stonebrew. But in recent expansions there has been some. TGT added a few original legendaries:

• Skycap'n Kragg
• Nexus-Champion Saraad
• Bolf Ramshield

And from League of Explorers these are original:

• Arch-Thief Rafaam
• Reno Jackson
• Elise Starseeker
• Sir Finley Mrrgglton

You can check the full list (including newer expansions, spells and other cards) in Hearthstone's wiki at Gamepedia.

Solution 2:

All of the legendary cards in Hearthstone are from Warcraft lore. All legendaries are specific characters, like a raid boss or unique weapon.