Nuno, who recently left his post as Wolves boss, recently held talks with Crystal Palace, but the Eagles pulled out after suspecting his head had been turned by Everton.
The Toffees have now agreed terms in principle with Nuno, something done on Friday evening, as he advances towards becoming their new manager.
There is no indication over the length of contract that Nuno will sign, but he is happy with the terms on offer from the Goodison Park outfit.
Everton are keen to bring in a new manager as soon as possible, having lost Carlo Ancelotti to Real Madrid.
They are now poised to appoint Nuno and will look to back the Portuguese tactician in the transfer market over the course of the summer.
Everton were linked with a number of managerial options, but have moved swiftly for Nuno after identifying him as their first choice.
For Nuno, taking the job at Goodison Park represents a swift return to the game following his departure from Wolves at the end of the season.