Sky Sports News understands the fee is comprised of £16.5m up front, with potential add-ons taking it closer to £24m.
Hackney has signed a five-year deal on Merseyside.
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The 24-year-old, who was named Sky Bet Championship Player of the Season for 2025/26, had only one year left on his deal at the Riverside Stadium.
Everton boss David Moyes had made signing a new No 6-type midfielder a priority this summer.
"Hayden is a promising young player who we've been tracking for some time, and I'm looking forward to working with him," said Moyes.
"We've had a track record over the years of identifying players in the Championship who have gone on to do really well for us and been good investments. We hope that will be the case with Hayden, too.
"He's an England U21 international who will provide greater competition in midfield, which is something I wanted going into the new season."
Everton's transfer dealings so far
In
Hayden Hackney - Middlesbrough, £24m
Merlin Rohl - Freiburg, £21.7m
Out
Isaac Heath - Cambridge, free
Seamus Coleman - released
Tyler Onyango - released
Idrissa Gueye - released
