Nelson, 26, picked up Aycliffe's Supporters' Player of the Season Award for the 2024/25 campaign, and arrives at the Towbar Express Stadium having previously represented Guisborough Town.
Whitby Town manager, Gary Liddle, said: "Alex joins us after another consistent season for Newton Aycliffe where he came away with a top award to show for it.
"He's a different type of defender to what we already have and has a great dedication to the game.
"He's quick, committed, and he's looking forward to testing himself at a higher level and I've no doubt he's got the characteristics to be a huge success.
"I'm really pleased to be able to add him to the squad."