Gibson's return will also be a welcome one for Martinez as it increases options in central midfield.
"Darron I consider fully fit," said the Toffees boss.
"He has been working extremely well and has joined the group so that is a great positive for us."
Striker Arouna Kone could also be involved after being left out at West Ham as he was not entirely right after a knee problem.
"He was 95% at the weekend and we didn't want to take the risk. Kone has a 99% chance he will be available," said Martinez.