LeGrand suffered a spinal cord injury in a game against Army in 2010. Initially told he would be a quadriplegic and would remain on a ventilator, the defensive tackle is now breathing on his own and can stand upright with the aid of a metal frame.
"I can relate to that because I am never giving up in my situation," LeGrand said in a telephone interview with The Associated Press. "I am never giving up in my situation. I know I will fight through it. Now getting this, this is a dream come true, especially on the 20th anniversary of the ESPYS. I was even thinking about it last year, thinking that could be me."
LeGrand plans to make the trip to Los Angeles for the award presentation on July 11.
LeGrand, 21, has vowed to walk again. The New Jersey native resumed his studies via video conferences last year and led the Scarlet Knights onto the field before a game last season.
In May, the Tampa Bay Buccaneers signed LeGrand to a symbolic contract. Bucs first-year coach Greg Schiano, who left Rutgers for Tamp Bay in January, invited LeGrand to address players earlier this month at the team's training complex.
Since suffering the injury, LeGrand has remained remarkably positive. He has been aggressive with his rehabilitation and works as an analyst on the pregame, halftime and postgame radio broadcasts of Rutgers games. He also will have a weekly show on Wednesday during the season with new Scarlet Knights coach Kyle Flood.
LeGrand admitted there are moments when he gets down, but they are rare.
"I have so much going on with my life, so many things that have happened, amazing things that I could only dream about," LeGrand said. "When I go to therapy every day, I look at people who don't have as much support as I have or are not getting the opportunities that I am getting, so how could I complain about anything.
"I have the whole world behind me now pushing for me. There is nothing for me to complain about. I have to keep fighting and getting better and help find a cure for this injury for many other people who are fighting to get back on their feet."
LeGrand also says every time he looks on Facebook or Twitter, there are people offering him encouragement.
"How can I get down when I am motivating all these people in the world," he said. "I see this as a responsibility to show that miracles can happen."
LeGrand would like to say when he will walk again "but I know it will happen and this will happen for a reason, and I will get up off this chair and walk again."
The Jimmy V Award is given to someone in sports who has overcome great obstacles through perseverance and determination. It is named for Jim Valvano, the North Carolina State coach who gave an emotional acceptance speech at the 1993 ESPYS that included his famous words "Don't Give Up ... Don't Ever Give Up!" He died of cancer later that year.
Information from The Associated Press was used in this report