The Scottish club said the 16-year-old goalkeeper, a former Melrose FC player, had left on a permanent transfer for a “substantial fee”.
Hibs said the deal for Vickery, who attended Earlston High School, also includes a sell-on clause.
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On the transfer, Hibernian sporting director Malky Mackay said: “Ben is a young player with a lot of potential, which is why there was a lot of interest in him from elite clubs below the border.
“Developing young players with this potential is credit to our staff and the Hibernian FC academy.
“When clubs like Manchester City show interest in one of our young players, understandably it becomes an opportunity that’s difficult for them to turn down.
Ben Vickery in action for Hibs _(Image: Maurice Dougan)_ “After Ben’s successful trial, we worked hard with Manchester City to get a deal that represented his true value rather than the player running his contract down and Hibs receiving the usual training compensation.
“We’d like to thank Manchester City for how they conducted themselves during the negotiations, and wish Ben all the best for the future.”
Vickery joined Hibs aged 10 and developed during his time in the club’s academy, going on to feature for Darren McGregor’s under-18s last season at just 15 years old.
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Alongside impressing in Hibs’ academy, the young ‘keeper has also been involved with Scotland’s youth set-up, featuring for their under-16s.
Vickery becomes the second Borderer to make the move from Hibernian to an English Premier League club this year.
Striker Josh Landers, from Innerleithen, signed for West Ham United at the start of the year.
The 18-year-old, who went to high school in Peebles, has been in action for Scotland’s U19s this month in Slovenia.