Tykes manager David Flitcroft had initially only been prepared to offer Steele a one-year contract, but that extended to two years after Mansford held discussions with the club's boss.
The 28-year-old told the Barnsley Chronicle: "I had an offer early on and it was a straight 'no'. After that, I said to my agent and family that I would look elsewhere if that was the best Barnsley could do.
"There were no mind games. I spoke to other clubs because I felt Barnsley weren't giving me anything to work with in terms of contract size.
"But once Ben came in, things changed and the offer improved so I stayed. Deep down, my family knew that I wanted to stay at Barnsley and I am relieved that it is all sorted and I'm excited for next season."
The former Manchester United trainee has made 178 league appearances for Barnsley since he joined the club in 2008.