Crosby is currently on crutches following off-season surgery, but insists he will be fit and available for Rhinos’ 2019 Betfred Super League opener at his previous club Warrington Wolves on Saturday, February 2.
That will mark the start of his three-year deal after he played seven games on loan at the end of last season.
Crosby spent six seasons with his hometown club, Wigan Warriors, winning two Grand Finals, before two years at Warrington Wolves.
His time there was overshadowed by the tragic death of his new-born daughter, Ada, last year and he spoke when he initially joined Leeds of making a fresh start.
Crosby, whose wife Megan gave birth to son Oscar in May, said: “That [a long-term deal] was the aim and as soon as I set foot in Kirkstall and Headingley I knew this was the club for me.
“I am looking to progress as a player – and as a person, more importantly – and I am just grateful for the opportunity the club have given me.
“I want to repay the faith they have shown in me. I feel I am coming into my prime now, my body’s ready and my best years are ahead of me.
“I am grateful to be at Leeds Rhinos and I will put my best foot forward.”
The length of the contract suggests Rhinos believe Crosby can become a mainstay of their pack as they enter a new era under coach Dave Furner.
“I thought I put some okay performances in last season,” he added.
“I just want to keep improving week-in and week-out and I am sure Leeds Rhinos are going to make me the player I can be.
“It is a clean start now. Last season it wasn’t the best circumstances when I came in and I got suspended which wasn’t ideal, but now the deal’s done I can look forward. There’s a bit of a new direction at the club, a few new faces and a few challenges ahead of us.
“Everyone’s excited, everyone’s bouncing at training and it is a really good atmosphere.”
Former Test and State of Origin front-rower Trent Merrin will join Rhinos next month in time to make his first appearance – alongside fellow recruits Konrad Hurrell and Tui Lolohea – in the Boxing Day challenge against Wakefield Trinity.
Merrin is Rhinos’ highest-profile signing for a decade and Crosby is looking forward to teaming up with someone who has achieved so much in the sport.
“I think the pack is looking really strong,” he said.
“He [Merrin] is a world-class player, he’s proved that for Australia, New South Wales and in the NRL and I can’t wait to learn from him and play with him.
“I think our pack’s going to be quite formidable next year with a full pre-season under Dave. We’ll get some new systems in place and new relationships going and we are looking quite strong.
“This time of year is all about building relationships with each other.”
Crosby is aiming to take more of a leadership role next year. He added: “I am 27 now so I am getting to an age now where I can do that.
“I pride myself on my professionalism and my attitude and if I can pass on any of my experiences to the young lads or the squad in general I will do that, but I just want to do my job for the team and if everyone does that we’ll go a long way to being successful this year.”
Crosby is confident the recent surgery will not hold him back. He explained: “I just needed a clean out at the end of the season.
“I played all last year with it, but the ankle needed doing.
“It’s just a minor setback and I should be ready for the start of the season.
“It’s a procedure I knew I had to have, it was just when I was going to have it.
“Now’s a good time and hopefully I can rest it up and I should be firing ready for the season.”