The defender is due to travel to Merseyside to meet with The Toffees on the weekend, as the deal has been tied to Everton defender Sean O'Hanlon signing with The Robins on a permanent basis following his initial arrival at Swindon on loan.
County Ground chief executive Mark Devlin sees Mills's move as a great opportunity for the youngster.
"Leigh Mills is a player of tremendous potential and we would not like to stand in his way of joining such a big Premiership side," Devlin told the club's official website.
"We have received a very good offer from Everton, which we have accepted.
"Swindon Town are keen to bring Sean O'Hanlon to The County Ground and it would make sense for the two deals to be tied together, and that is what the two clubs will be working on over the next few days."
