The 25-year-old Albanian striker arrives from Catania on a loan deal with a view to a permanent deal.
United have been chasing the player’s signature throughout the month and he is delighted to be in West Yorkshire.
He told the club website: “I heard about a month ago that Leeds wanted me. I was very happy about that and I’m very happy to be here.
“I think it is a great team. I think that we can keep going like this, like these last two matches that we won.
“I would like to play and do as much for the team as I can.
“I’m a good header and I like to move in the forward areas. I like to keep the ball and to let the team go forward.”
Cani was born in the Albanian capital Tirana but has spent most of his playing career in Italy. He started out at Pescara and also played for Palermo before playing for Polish club Polonia Warsaw.
He has become United’s third addition of the January transfer window after Sol Bamba and Granddi Ngoyi.