The 37-year-old retired from playing at the end of the 2017 season, winning an eighth Super League Grand Final in his last game.
The father of three made his debut in 2001 and played 492 times for Leeds, placing him in fifth in the club’s all-time list of career appearances.
He scored 196 tries and a total of 1,103 points and won 15 England caps, as well as five Test appearances for Great Britain.
Breaking the shock news, Burrow said: “Regrettably, today I am confirming that I have been diagnosed with motor neurone disease.
“I would like to thank everyone for the support I have received already since being given my diagnosis.
“I know I have a big challenge in front of me, but knowing that I have the love and support of so many people will give me inspiration and strength.”
Burrow added: “I am very positive about the situation and intend to battle the condition as I still feel fit and well.
“I would like to ask for privacy at this time so I can adjust to the battle I have ahead and so that I can spend time with those closest to me ahead of Christmas and New Year.”
In those living with MND, messages from the motor neurones gradually stop reaching the muscles. This leads the muscles to weaken, stiffen and waste and those affected may lose the ability to walk, talk, eat, drink and ultimately to breathe. MND affects everyone differently and not all symptoms will affect everyone or in the same order.
The MND Association's director of external affairs Chris James said: "Sadly there is currently no cure for MND and there is only one treatment, which in some cases has been shown to extend life expectancy by up to three months.
"People with MND can be given techniques to limit the impact of the disease on daily life, this could include dietary advice, physiotherapy and occupational therapy.”
Rhinos director of rugby Kevin Sinfield is a former team-mate of Burrow.
“This has been devastating news and heart breaking for Rob and his young family,” Sinfield said.
“The thoughts of everyone at Leeds Rhinos and, I am sure, throughout the rugby league family, are with Rob and his wife Lindsey.
“Throughout his career, Rob overcame the odds to become a legend of the game and I know he will tackle this challenge with the exact same positive determination.”
Sinfield went on: “As a club, Rob will receive our full support and we will be working with him to chart the way forward.
“I would like to thank [former Scotland rugby union player] Doddie Weir for taking time out recently to meet with Rob and talk about his own personal experiences with MND.
“The news has been a massive shock and I know it will be similar for his many former teammates, friends and fans in the game.
“We will be developing ways we can best support Rob and his family in the future over the next few weeks and will be hoping to announce plans as soon as possible in the New Year.
“In the meantime, I would ask you all to keep Rob and his family in your thoughts over the festive period.”
Jamie Jones-Buchanan’s testimonial game against Bradford Bulls at Headingley on Sunday, January 12, will now be a joint fund-raiser for Jones-Buchanan and Burrow and tickets are now on sale.
A Virgin Money giving page has been set up at www.virginmoneygiving.com/fund/robburrow with all donations going to the fund.
Supporters wanting to organise their own fund-raising should email [email protected] and the club will respond in January.