A two-time Grand Final winner, Crosby, 27, has joined Rhinos from Warrington Wolves on a loan deal until the end of the season.
Rhinos’ director of Rugby Kevin Sinfield said: “We are delighted to be able to bring a player of Dom’s experience into our group.
“He has spent some time around the lads and I know he is keen to get out there and show what he can do in a Rhinos shirt.”
Crosby said: “I am really looking to playing the Rhinos and getting out there with the boys tomorrow night.
“It is an exciting time for the club with a new management team in place and hopefully I can come in and help the team out where I can.”
Crosby has spent the last two seasons at Warrington.
He joined the Wigan Academy in 2010 from Hindley and, after dual-registration spells with Widnes Vikings and South Wales Scorpions, made his first team debut in a Challenge Cup tie against North Wales Crusaders in 2012.
Crosby, who has also played for Leigh under dual-registration, scored seven tries in made 102 appearances for Wigan before joining Warrington last year.
He played seven times in 2017 and has made ten appearances this term, but is out of contract at the end of the current season.
Crosby will not be allowed to play for Leeds in next month’s Ladbrokes Challenge Cup semi-final or against Warrington in the Super-8s, if Rhinos qualify.
Rhinos have been linked with a move for their former player Paul Aiton, but he has not been included in the squad to face Widnes.
The transfer deadline for the 2018 season is Friday, July 27.