Smith, 23, left the Rhinos after helping them to a third consecutive Super League Grand Final triumph in October, having made more than 100 appearances for his hometown club.
He said: “It is a dream come true to get another opportunity to play for the Rhinos and pull on a blue and amber shirt again. I genuinely believed that my last game for the Rhinos would be last year’s Grand Final at Old Trafford and that was an emotional occasion for me.
“Unfortunately things did not work out for me at Wasps but I am grateful to them for allowing me to return home and move on to the next stage of my career. I always said that if I did return to Rugby League that Leeds was the only club I was interested in playing for and I am grateful to Paul Caddick, Gary Hetherington and Brian McClennan for allowing me another opportunity to play for my club.”
Smith made just two appearances for Wasps, with a further two run-outs for their A team. He will go straight into the Leeds squad for their derby game against Bradford on Thursday.
He added: “I can’t wait to get a game under my belt. It has been frustrating because all players just want to play rugby. On paper eight rounds of the competition doesn’t sound like that long of time away but it feels like ages because of the move to London and the big change in my life.
“I think I will appreciate things a lot more now having had the experience of moving away and working in a different environment. Leeds was all I knew when I left here but I am glad to be back. I can’t wait to run out at Headingley Carnegie again, that is something that I thought I may not get the chance to do again in a Leeds shirt so it will be very special.”
Smith’s last appearance in rugby league came for England in the end of season Four Nations, before completing his move to Wasps on a three-year deal, making his debut against Newcastle in February.
Head Coach Brian McClennan said: “We are delighted to welcome Lee back into our family. At the end of last season, he went with our best wishes to try a new challenge in his life. At just 23 years of age, he has his whole career hopefully in front of him. We are delighted to have him back at Leeds especially on a long term contract.”