Ameobi has signed a two-year deal with the option of a third, with the Newcastle-born player having returned to his native north east after leaving Nottingham Forest.
He joins the club on a free transfer.
The 29-year-old, who spent a loan spell at Boro in 2013, will provide a welcome new addition on the flanks following the departure of loan players Yannick Bolaise and Neeskens Kebano and also Marvin Johnson and Nathaniel Mendez-Laing.
On signing the former Newcastle United and Bolton Wanderers player, Warnock said: “As soon as I became aware Sammy was available I let him know I wanted him, and we had a few good conversations.
"I thought it was important he could see what he could do for us, and what I could do for him.
"I've always thought he's a danger, and I'll be looking to use that danger and have a system where I can get him in positive forward positions."
Ameobi has become Boro's second signing of the close season following the earlier arrival of QPR goalkeeper Joe Lumley.