There was significant interest from elsewhere in the 31-year-old, with his former club Sheffield Wednesday one of those in the race.
Batth has opted to join the Black Cats on an 18-month deal, becoming the second signing of the January transfer window after Trai Hume. Sunderland have not paid a fee.
Johnson says that he has twice signed to sign Batth in the past, who has twice promotion from League One.
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The Sunderland head coach has cited his leadership qualities as potentially crucial for the second half of the season.
“Danny is a player that I’ve tried to sign a couple of times before, so it’s third time lucky,” Johnson said.
“We have some good characters already in place at the football club and you are always looking to nurture leadership qualities, but Danny’s come ready-made.
“A dominant centre back, he has a great personality and I think he will have really positive effect on and off the pitch.”
Batth has featured for Stoke City in the Championship this season, but the recent arrivals of centre-backs Phil Jagielka and Taylor Harwood-Bellis had pushed him down the pecking order.
He says he is excited to have joined a ‘juggernaut’ of a club.
"This is a juggernaut of a football club and I’m delighted to be a part of its journey.
"This is the perfect set-up for me. I’m really looking forward to playing in front of the home supporters and I’ve already spoken to the Head Coach, who has tried to sign me in the past.
"When the opportunity arose, I thought it would be the perfect option to crack on and do well.”
Batth will be available for selection when the Black Cats face Portsmouth at the Stadium of Light on Saturday afternoon, and thus significantly strengthens Johnson’s options.
He should also be able to call upon Carl Winchester and Corry Evans for the game, and remains in the market for further recruits.
A striker and an attacking midfielder as a minimum are expected before the window shuts.