Martinez admitted it wasn't easy for him to make the move, but that Los Leones had tried hard to get him.
The central defender has been accused of hypocrisy after a video emerged of him saying he would never play for a rival.
"Athletic made it very clear they wanted me," he said to reporters.
"It hasn't been easy to make the move but I'm happy and thankful to this club.
"I'll give the best of myself and contribute everything I have to continue adding value to the squad.
"That's the best I can do."