The 18-year-old right-back passed a medical, agreed personal terms and penned his contract after the clubs agreed an undisclosed fee.
He told evertonfc.com: "I am very excited to be joining Everton. I've been very impressed with everything I have seen at Finch Farm already. Now the hard work begins."
The 6ft 2in England Under-19 international made his Tykes debut last March after progressing through the youth ranks at Oakwell.
He featured 28 times for the npower Championship club, netting his first goal in the 4-3 Capital One Cup triumph over Rochdale in August.
Stones added on barnsleyfc.co.uk: "I would like to take this opportunity of thanking everybody at Barnsley for helping me in my development.
"They include Ronnie Branson and all the academy staff; Keith Hill and David Flitcroft for giving me the chance to play first-team football. Also all the backroom staff such as Guy Proctor, John Lucas and Craig Sedgwick.
"They are just some of the people who I owe a debt of gratitude to and I wish Barnsley every success for the future."
Source: PA
Source: PA