Martinez made the move yesterday to the tune of €15.5m.
He stated: "Dear Genoans, it is difficult to explain in a few words what these two years spent with you have meant to me.
"I arrived at a difficult moment for the club, with the clear objective of bringing Genoa back to where it deserves, in Serie A. Together, we managed to reach this goal against Ascoli, a moment that will remain among the best of my career. Furthermore, this year we were the best newly promoted team in Europe, a result we can all be proud of.
"After these two years rich in unforgettable experiences, the time has come to make a difficult decision and part ways. I will miss cheering in a dream stadium, feeling the warmth of every sector, from the North Stand to the South Stand. I will always remember your unconditional support and kindness, energy that you transmitted with every Genoa goal.
"I am very proud to have been part of the Genoa family and I will never forget you. I want to conclude by thanking all the people who work within the club for making me feel at home in these two years: warehouse workers, cooks, physiotherapists, coaches and teammates. Thank you, Genoa. Thanks, Genoans. You will always be in my heart. I love you.
"With love, Josep Martínez."