Mendeika, 23, came through the academy ranks at Warrington and has also had spells with Leigh, Swinton and London.
He said: “I am absolutely over the moon to be joining Bradford, I feel extremely privileged and cannot wait to get going.
“It is great to be back within a full-time environment and I am looking forward to repaying the faith the club has shown in me.
“James Lowes is a great coach and I am excited to be working under him again, he will really develop my game.
“I came here because I believe in the direction the club is heading in. Where the Bulls might well be in a couple of years’ time excites me and I want to be a part of it.”
Lowes handed Mendeika his Warrington debut during his stint as head coach at the Halliwell Jones Stadium, in a friendly against Wigan, while the versatile centre featured at fullback and stand-off for Ireland in their World Cup games against England, Australia and Fiji at the back end of 2013.
Lowes said: “James is a very talented, up and coming player and we are pleased to have secured his services.
“I had him at Warrington and was very impressed with what he had to offer then.
“Injuries have set him back a little over the past couple of years but he has a long career ahead and he is certainly looking to make a name for himself here.
“He has trained once with the boys this week and I am sure he will settle in well.”