The ex-Scotland defender, who managed the national team from January 2008 to November 2009, was diagnosed after feeling unwell earlier this year.
Burley, 68, played for Ipswich from 1973 to 1985 and completed 500 appearances for the club. He was manager at Ipswich from 1994 to 2002.
“It has been a difficult time, but I am feeling much brighter now,” Burley said. “In fact, I am able to get to matches at Portman Road and I am enjoying watching the team playing back in the Premier League.
“We are grateful to the club for the support they have shown me and my family and I would ask that everyone is respectful of our privacy at this time.”
Burley also competed for the likes of Motherwell, Ayr United and Falkirk.
As a manager, he coached clubs including Crystal Palace, Hearts and Southampton.
He was the last manager to guide Ipswich to Premier League promotion before current boss Kieran McKenna did so last season.
McKenna said: “This club has had some brilliant managers and George is right up there as one of the very best.
“It has been a pleasure to get to know George since I arrived at Ipswich. He is a positive and optimistic character, and I know he will also take that attitude into the battle he now faces. We are all right behind him.”
Club chairman Mark Ashton added: “Our thoughts are with George, his wife Jill and their family.
“It’s always great to see him here in the directors’ box on a matchday and we will do everything we can to support one of our all-time greats, uniquely as both player and manager.”