Steele, whose move has been confirmed after he passed a medical in Athens, spent five years at Oakwell after making a memorable debut in the Reds' fifth-round FA Cup win at Liverpool in February 2008.
"I promised my family at this World Cup that this next four years is really important to me and I want to give everything I've got to get as close as I can to that set-up (England)," Steele told the club's official website.
"I've had to think about my career and moving on. Whoever even mentions money to me as being a reason is a foolish man because I can assure you it's nothing to do with that."
Steele started out at Peterborough before Manchester United paid £500,000 for the then teenager in 2002, but he failed to make a first-team appearance at Old Trafford.
After two loan spells at Coventry he moved on to West Brom in 2006 and joined Barnsley, initially on loan, in 2008. He made 227 appearances for the Reds.
"I want the fans to know how hard this decision was," he added. "It was the hardest decision in football that I've ever had to make.
"There were times when I thought I'd be here forever and I really did want to break all the records and play longer than anyone else.
"That made it more emotional for me to leave. Leaving is huge and I want to thank all of the fans for being so good with me from the start."
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