The Toffees have been linked with the 19-year-old all summer and The Guardian say they will pay the Italian side a fee of £29million.
It is claimed the final figure could rise by a further £9m with add-ons but that Everton have managed to come to an agreement without inserting a buy-back clause.
Instead, Juve will be informed of any bids from other clubs in the future and will have the option to make it.
The agreement marks a massive coup for Everton who will be signing one of the most highly-rated attackers in Europe.
Kean burst on to the scene last season as with six goals 13 Serie A appearances – just five of them start.
He has since gone on to break into the Italy national team squad and has won three caps under manager Roberto Mancini.
Toffees boss Marco Silva has been keen to strengthen his forward line as both Cenk Tosun and Dominic Calvert-Lewin struggled for goals last term.
Silva’s business is unlikely to stop at the signing of Kean as he might need to go back into the market for a replacement for Idriss Gueye.
The midfielder joined Paris Saint-Germain in a £27m deal on Monday after failing to secure a move in the January window.
Everton have already signed Fabian Delph from Manchester City but have been linked with the likes of Mario Lemina from Southampton.
They have also bid for Crystal Palace star Wilfried Zaha but that was rejected and the signing ion Kean could signal the end of their interest.
Meanwhile, Gueye paid tribute to the Merseyside club in an emotional Instagram post after sealing his switch to PSG.
“As you know I am about to start a new journey, a journey that I have dreamed about since a kid and when this opportunity presented itself I couldn’t turn it down.”
On moving to PSG, he said: “I will do everything to justify the faith [PSG] have shown in me and to integrate into this talented squad.”
Gueye made 108 appearances in three seasons at Goodison Park after moving from Aston Villa in 2016.
