Stones' place in England's starting XI has been questioned.
“He hadn't made his debut when I joined Everton that summer, but, from day one, I knew John had to be a centre-half and he had the composure on the ball to play there.
“It was a really interesting journey to see him grow and taking responsibility and get to the level he has got to. He has a big future."
Stones is the only member of Gareth Southgate's World Cup squad that Martinez worked with during his time in charge of Swansea, Wigan and Everton, although he admits there was one other he was looking to sign.
Martinez said: “We followed Kieran Trippier for a while – my chief scout loved him, absolutely loved him."