The 66-year-old has stepped down after 30 years at the helm of live sports broadcasting for the BBC.
During a discussion about Novak Djokovic's victory over Nick Kyrgios in Sunday's men's singles final, former British number one Tim Henman interrupted Barker to show her a montage looking back on her career with tributes from current and former players.
Eight-time Wimbledon champion Federer said "You made me cry", while Murray said "You are going to be missed by everyone who loves tennis".
By the end Barker was wiping her tears with a tissue, with Henman's arm around her as Billie Jean King declared her to be the greatest presenter.
"She's an amazing example - if you want to be an amazing presenter, if you want to be anything in broadcasting - she's the GOAT [greatest of all time]," the American 12-time Grand Slam singles champion said.
Three-time Wimbledon champion John McEnroe, who had earlier given Barker "one last hug" on Centre Court before the men's final, told Barker she was "the Roger Federer of the broadcasting world".
Crowds had gathered near the roof-top studio where Barker had been watching the video and they burst into chants of "Sue! Sue! Sue! Sue!" and sang "we love you Sue, we do!"
Barker has presented a range of major events across the BBC - including Wimbledon and Queens tennis, Olympic Games, Commonwealth Games, World Athletics Championships, the London Marathon, the Grand National, Royal Ascot and Sports Personality of the Year.
A former world number three tennis player, who won the 1976 French Open title, Barker also reached the 1977 Wimbledon semi-finals before embarking on a broadcasting career that included presenting huge moments like Murray becoming Britain's first male Wimbledon champion in 77 years in 2013.
"It's been an absolute privilege - I've loved it, 30 amazing years, thank you," she said.
"I'll miss the job, I wish I had the next 30 years because I love it but most of all I'm going to miss the people I work with in front of the camera, behind the camera . You've just been absolutely amazing.
"I've just been so proud to front the programme. Thank you."