The Toffees have received the paperwork they need to bring the 23-year-old to Goodison Park on a contract until the end of the season and will now complete the formalities of the deal with the French club.
"Everton confirm they have been granted a work permit for Lacina Traore," said a spokesman.
"Talks are ongoing with Monaco to secure the 23-year-old's services."
Manager Roberto Martinez publicly confirmed their interest following Monday's 1-1 draw at West Brom, saying: "Lacina is a player who I really like and is someone who would fit in really well in the role we want the player to come in.
"He is a very talented footballer. He is only 23 and has already had a couple of moves (totalling) nearly £30million, but every work permit is a difficult one and we will try our best."
The 6ft 8ins striker is being brought in to replace Nikica Jelavic, who was sold to Hull last week, and will provide support for fellow on-loan forward Romelu Lukaku, who is currently Martinez's first choice.
Lukaku provided the knock-down for Kevin Mirallas to score the opening goal in the 1-1 draw at the Hawthorns, only for Uruguay international Diego Lugano to register his first goal in English football to secure a point for the Baggies.
"We lost two points, you have to be realistic," said Lukaku.
"In the first half we dominated but we didn't control the game as we should have done, and we have to learn from it and do better in the next few games."
On his return to the Hawthorns, where he spent last season on loan scoring 17 goals, Lukaku told evertontv: "I had a great time at West Brom and I hope they enjoyed my football and I left some good memories at the club.
"Now I am trying to do the same at Everton, but in a better way because I want to improve and become a better player year after year."
Injuries are continuing to affect the squad, and with midfielder Steven Pienaar absent with a groin issue against West Brom, Martinez lost full-back Seamus Coleman to a hamstring problem.
Everton will assess the Republic of Ireland international over the next 24 hours, but he could miss next Tuesday's Merseyside derby at Anfield.
"The next 24 hours are going to be vital to find out how he feels," said Martinez.
"Seamus is a really fit boy, so when he got that feeling something was wrong with his hamstring we needed to take that seriously.
"We will find out over the next few hours the extent of the injury.
"Steven Pienaar had to come off against Norwich and since then he has been working hard to get back to full fitness and it was a little bit short for Monday.
"We will assess him over the next few days. It shouldn't be too big a problem in his groin area."
On the upside, Martinez hopes to have Gerard Deulofeu back from a hamstring injury soon, as the on-loan Barcelona youngster has been out of action since December 14.
"Gerard is progressing really well. A member of our medical department went over to Barcelona to find out where he is (in terms of fitness)," the manager added.
"It is a bit more complicated injury because it affects the tendon and that can get re-injured very easily.
"We are happy with his progress and he is doing really well and I don't think it will be long before he is back.
"We reassess him every three days. Hopefully he will carry on with no setbacks."