The 19-year-old midfielder will be loaned back to the Scottish Championship side until January - subject to paperwork approval from the Scottish Football Association - to continue his development before joining Hibs at the start of 2022.
Hibs head coach Jack Ross told the club's official website: "Dylan is someone that we identified last season as a young player with enormous potential.
"He continued to show his ability in Raith's early fixtures, and my staff and I are excited about working with him and continuing to develop his game."
"I'm delighted," said Tait after agreeing a four-year deal.
"It's a massive club and I can't wait to get going.
"I've been playing for Raith Rovers in League 1 and the Championship, so this is obviously a massive step up for me, but I'm over the moon to get here.
"I want to continue my form over the next few months and keep impressing the manager here, so when I come back in January the manager will give me a chance. I want to kick on and keep improving."
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