The former Wigan manager, who succeeded David Moyes at Goodison Park in June, will take his side to Carrow Road when the new season starts of August 17.
West Brom will be Martinez's first home opponents, and the third fixture will see Everton travel to south Wales to take on newly-promoted Cardiff City.
Martinez's first Merseyside derby will be on home soil when Liverpool make the short trip across Stanley Park on November 23, with the return fixture at Anfield on 28 January.
Everton will take on Premier League champions Man United and their former boss Moyes at Old Trafford on December 3, at the start of a busy month which sees a trip to Arsenal four days later.
The Toffees are at home to Sunderland on Boxing Day with Southampton visiting Goodison Park on December 28.
David Moyes will return to his old club when Man United visit Everton on April 19.
Everton's season concludes when they face Hull City away on May 11.