The Dutch manager is expected to join Everton shortly.
The Dutch manager, currently at Southamton, is expected to sign a contract with the Merseyside club today as the semi-saga reaches its conclusion.
Everton will have to pay around £5 million to the Saints for compensation.
Former Valencia boss Koeman has enjoyed an excellent couple of years in England, leading Southampton to a 7th-placed finish in his first campaign of 2014-15, before going one better than that this past season.
It was reported (Mirror) that the 53-year-old would also be given a £100 million warchest by new Everton owner Farhad Moshiri, and Nevin, who spent four years with the club, says most Toffees fans he has spoken to are delighted with the acquisition.
"Most Everton fans I've spoken to have definitely accepted him," Nevin told BBC. "His recent record and career in England has looked very, very good indeed.
"They're absolutely delighted with it and it should be very good."
Should it materialise, Koeman's first two jobs will be simple: whether he can keep John Stones and Romelu Lukaku for one more season at least.
Retaining Stones may be easier, given that striker Lukaku revealed in no uncertain terms that he wanted to leave the Goodison Park club this summer (Sky Sports).