Bryant, 41, died on Sunday in a crash close to the city of Calabasas in Los Angeles County, California.
Eight others on board, including his 13-year-old daughter Gianna, also lost their lives.
Following the initial reports of Bryant's passing, athletes and teams from across the world of sport posted their tributes to the Lakers great on social media.
New England Patriots great Brady wrote on his Twitter page: "We miss you already, Kobe."
Patrick Mahomes, another superstar NFL quarterback, said: "Man, not Kobe. Prayers to his family and friends!"
Bryant was an Olympic champion like Usain Bolt, the great sprinter, who posted a picture of the former NBA star on his page.
"Still can't believe [it] @kobebryant," he said.
World number one golfer Brooks Koepka posted a lengthy message in memory of his "hero".
"Kobe Bryant was my HERO growing up. Even to this day he was an inspiration to the way I approached things," he wrote, adding: "His mentality motivated me not only in hard times but throughout my whole life. RIP, Kobe."
Footballer Raheem Sterling said: "Rest easy, legend."
Meanwhile, Neymar, who scored twice in Paris Saint-Germain's win over Lille on Sunday, dedicated his second goal to the Lakers legend.
Drew Brees spoke to ESPN from the Pro Bowl, saying of Bryant: "I had the chance to meet him one time. He was a guy I hoped to have the chance to be around more.
"I had so much respect for him as a competitor. I know he inspired so many people in so many different ways.
"He was one of the great competitors of any generation - not just with sports but the way he approached a lot of things with what he was doing now after basketball.
"I pray for him, I pray for his family. It's a tragic loss."
At seven under par for the tournament, Mickelson holds a one-stroke lead over his countryman entering the final round at Kiawah Island's Ocean Course after saving par on 18 while Koepka bogeyed the last.
The 50-year-old Mickelson is the fourth player aged 50 or older to lead a major after three rounds in the modern era, which began in 1934.
The others were Tom Watson at the 2009 Open Championship, Greg Norman at the 2008 Open, and Julius Boros at the 1973 US Open -- none of whom ended up holding on for the win.
Mickelson has been resilient this week in South Carolina, though, steadying himself Saturday after going bogey-double bogey on 12 and 13 to make par on the final five holes.
While Mickelson's resurgence has excited the fans, Koepka remains a model of consistency at the PGA.
He has finished at least tied for fourth in 12 of the last 13 rounds at the major, and he could become the first player to win the same major three times in a four-year stretch since Watson won the Open in 1980, 1982 and 1983.
Mickelson will be shooting for his sixth major title and first since the 2013 Open, while Koepka seeks his fifth.
Louis Oosthuizen, who shared the lead with Mickelson entering play Saturday, managed just three birdies on the day on the way to an even-par 72 that left him five under for the tournament.
American Kevin Streelman (70) is at four under, while Oosthuizen's South African countrymen Branden Grace and Christiaan Bezuidenhout are at three under after even-par rounds of their own.
Bryson DeChambeau (71) was unable to gain ground on the leaders and enters Sunday five back of Mickelson along with Gary Woodland (72) and Joaquin Niemann (71).
Jordan Spieth matched Billy Horschel for the low round of the day with a 68, and he sits at even par for the tournament along with Rickie Fowler (69) and Keegan Bradley (72).
Reigning Masters champion Hideki Matsuyama fell from contention with a 76, putting him at one over with the likes of Shane Lowry (73), Padraig Harrington (73) and Ian Poulter (73).
