The Irish midfielder played under the Spanish manager during their time at Wigan Athletic, before Martinez was appointed as the Toffees' new boss at the start of the summer.
However, Martinez secured the signing of McCarthy late on transfer deadline day, and the 22-year-old is delighted to be at Goodison Park.
"It is great to be here with him and hopefully I can stamp my authority on the team and get as many starts under my belt as possible," McCarthy told reporters.
"There are a lot of big names here. If I need to bide my time, I will bide my time."
McCarthy started every Premier League match for Wigan under Martinez last term.