Coady, 22, began his career playing in the Rugby League Conference but then switched to the 15-man code while studying at Loughborough University.
He will be loaned back to Doncaster, currently in administration, for the rest of the season, but Leeds see him as a possible long-term successor to Keith Senior.
“Keith is one of the world’s best centres so training and talking to him will be a big boost to me and help me adapt to life at the Rhinos,” he said.
“It has all come about pretty quickly. I am looking forward to training in a professional environment with the great players that Leeds have. That can only help me develop my game and reach my full potential.”
Head Coach Brian McClennan said: “Michael is a work in progress but a very exciting prospect.
“He is a raw talent but he is physical, tough, brave, athletic and, most importantly, intelligent so I am sure he has all the attributes needed to make a success of his opportunity.
“He is a difficult player to tackle and can break the line so you can see why the comparisons to Keith have been made. If he achieves half as much as Keith has done during his career, we will be more than happy.”