The Leeds-born wicketkeeper entered the record books in 2011 when he lined up against Durham University just 27 days after his 15th birthday.
But that match proved to be his only appearance at senior level and he never again progressed from the second XI.
In his last game for the second string he did not bat or keep wicket, instead sending down 3.3 overs for 29 runs.
“This was a difficult decision to make,” the 19-year-old said.
“I would like to thank the players and staff at Yorkshire for their support. I have been involved with the club since I was 11 and I feel that now is the right time for me to look at a career change.
“The support from my parents has been tremendous and I would like to thank Ralph Middlebrook at Pudsey Congs Cricket Club and England coach Paul Farbrace, who I had close working relationships with.”
Yorkshire’s director of cricket development Ian Dews, said: “Everyone at the club wishes Barney well.
“It is very much his decision. We hope that the next chapter in his life is very successful.”