Fairweather died on Monday evening surrounded by his family and loved ones. He was 63.
In a heartfelt statement Sunderland said: “The club has lost an exceptionally talented coach and an even greater friend, who impacted and inspired so many with his vibrant spirit and infectious smile.
“From players and staff to supporters, Carlton will forever be remembered on Wearside by all fortunate enough to cross his path.”
Sunderland’s Under-18s scheduled game against Wolves on Tuesday was cancelled out of respect.
Fairweather held a variety of roles during his time with the club that lasted more than two decades.
Having been a member of Wimbledon’s famed ‘Crazy Gang’ during his playing days, Fairweather joined Sunderland in 2003 and initially spent time as boss of the club’s women’s team. He later moved into the academy system, where Sunderland say he “made a remarkable impact”.
Speakman, Sunderland’s sporting director, said: “Carlton’s personality and charisma was unique. He worked across all aspects of our club and the reason he’s so highly thought of is down to his dedication, humility, and work ethic.
“Within a sporting environment, you need consistency, and Carlton’s character very rarely shifted from enthusiastic, bubbly, and infectious.
“Add this to someone who crafted their skill of coaching and mentoring over so many years and it’s a special mix.
“I was blessed to spend time with Carlton on many occasions and he always brought the gift of wisdom, a gift only very few people can give. He will be truly missed by all within our club.”
Sunderland paid tribute to Fairweather during the recent Championship game with Preston at the Stadium of Light. The players warmed up wearing ‘For Carlton’ t-shirts and Fairweather was then given a guard of honour by club staff as he was welcomed onto the Stadium of Light pitch.
Ahead of that game, captain Dan Neil said: “Carlton has had a massive influence on my personal development coming up through the academy and I know it’s the same for many others who came through.
“Many of those are in the first team now and others who have gone on to play for other teams.
“His personality in and around the building was amazing. He lights up whatever room he comes into, and he has an infectious smile and laugh.”
Robin Nicholls, academy manager, said before the Preston tribute: “Carlton is an infectious character. His dedication to this football club is outstanding and the longevity of his service is something to be admired.
“In a world where change is constant, Carlton serves as a true reminder of the impact that a single person can have on an organisation.
“Hundreds of players that have come through this building have been impacted by not only his coaching, but his character and expectations of being a good human being.
“His legacy will continue with the impact that remains in each member of staff that has worked with him during his two decades of service to SAFC.”
After his passing, Sunderland said: “The thoughts and prayers of everyone at Sunderland AFC are with Carlton’s wife, Lesley, his children Jordan, Elliott and Tyla, and everybody who knew and loved him.”
