The 28-year-old appeared to be on his way out of Oakwell after expressing his disappointment at being offered a one-year extension to his contract.
David Flitcroft, who took over as manager at the Yorkshire club in December 2012, was originally only prepared to offer Steele a new one-season deal.
But Mansford persuaded Flitcroft to double the period to two and Steele 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."
Steele first played for Barnsley in February 2008 and has since gone on to make more than 190 first team appearances.