The England international has been strongly linked with a move to a top Premier League club before the start of next season, and it appears that the Toffees have won the race for his signature.
It had previously been reported that a move could be completed by the end of the week, and according to the Burnley Express, Keane will not be taking part during the early stages of pre-season with the Clarets.
The latest development appears to mark the end of Keane's time at Turf Moor, where he has played his football since September 2014 when he initially penned a loan deal from Manchester United before signing on a permanent basis.
United had been in the running to hand the 24-year-old a return to Old Trafford, but it has suggested in the past that the signing of Victor Lindelof led to Keane favouring a move elsewhere.
However, United will still benefit from any potential move due to a sell-on clause being inserted in his contract at Burnley.