"I always said that, if I did return to rugby league, Leeds were 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.
"I was nervous coming back to Headingley and felt a bit sheepish but it was great to get back on the training pitch and into the banter.
"The players have been good, but I feel I need to win their respect back as I left them last season."
Smith made just two appearances in the Wasps first team, as well as a further two appearances in the A team.
And he could now be in line for a dramatic return to action for the injury-hit Rhinos for Thursday's derby against Bradford Bulls after being drafted into the match-day squad.
"I can't wait to get a game under my belt," Smith added. "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 stayed in contact with the Leeds lads and we would speak at least once a week. I've been following the team this year and hopefully I can help out.
"I went to the Melbourne game at Elland Road and it was very tough sitting in the stand watching my team on the field.
At just 23 years of age, he has his whole career hopefully in front of him
Rhinos coach Brian McClennan
"I can't wait to run out at Headingley again. That is something I thought I may not get the chance to do again in a Leeds shirt so it will be very special."
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."
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