The number has been worn for years by Kevin Sinfield, who has retired from top level rugby and is now playing second-tier rugby union with Yorkshire Carnegie.
The 21-year-old Ward has also agreed a new five-year deal with the Rhinos, and he is looking forward to taking his career to the next level/
“I am immensely proud that the club have decided to give me the number 13 squad number,” he said.
“Iit is a dream come true. I was six when Kev first wore it so that is all I have ever known and it is an honour to receive the number after him.
“Growing up supporting the Rhinos, it was my dream to play for Leeds but it was always the number 13 shirt that I wanted to wear.
“I was really pleased with how last season went for me, it was my most consistent season so far. Since I suffered the injury, it has obviously been frustrating but I am positive about the future.
“The injury was complicated so things have had to take their natural course. I will have the operation on my knee on Monday and it will be assessed after that how long I will be out for.
“This has been a massive boost for me as I look ahead to the next few months and getting myself back fully fit.
“I was delighted to sign my new contract as well. There is a great group of young players here at the club who have committed to each other, and the club, to take the Rhinos forward over the next few years.
“The club have continued to show faith in the young players and rewarded them with long term deals so we can build something special together.
“Inevitably that will take time but we know from recent history the benefits that brings.”
Leeds head coach Brian McDermott is looking forward to seeing a fully fit Ward in action soon.
“I am really pleased for Stevie, he thoroughly deserves his new contract and the number 13 squad number,” he said.
“Inevitably people will talk about taking over from Kevin in that number but Stevie is a different player and person and the pressure he puts on himself to perform for Leeds every time he steps on the field will not change just because he is wearing 13 instead of 14.
“He has got a tough few months ahead of him now but he is the best possible hands with our medical team and I am sure he will be a great addition to our squad when he is finally fit next season.”