Are there any legendary characters created specifically for Hearthstone?

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.

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