"Congratulations, Tiger!" tweeted Barack Obama. "To come back and win the Masters after all the highs and lows is a testament to excellence, grit, and determination."
"Congratulations to @TigerWoods," tweeted the White House incumbent Donald Trump, who played a round of golf with Woods earlier this year. "A truly Great Champion!"
The Masters, the PGA Championships, the US Open and the British Open are considered the major prizes on the golfing circuit.
Woods won his first at the Masters in 1997 and the 21-year-old prodigy famously hugged his father, Earl, after the triumph.
On Sunday, Woods terminated an 11-year drought without a major with a dramatic win.
The 43-year-old started the fourth and final day at the Augusta National two shots behind the pacesetter Francesco Molinari but he completed the 18 holes in 70 shots to finish with an overall total of 275 shots.
Woods' compatriots Brooks Koepka, Dustin Johnson and Xander Schauffele all ended on 276.
Woods, who underwent spinal fusion surgery in 2017 due to chronic back pain, said: "It's overwhelming just because of what has transpired. I could barely walk. Couldn't sleep. Couldn't walk. Couldn't do anything.
"To have the opportunity to come back, it's one of the biggest wins I've ever had for sure."
Woods claimed his last major at the 2008 US Open. Soon after that triumph, tales of his sex binges with an array of women were splashed across the media. His wife, Elin Nordegren, and sponsors deserted him as did his fabled prowess on the golf courses. A spate of demoralising knee and back injuries compounded the woes.
But he has tasted redemption. As well as picking up a cheque for 1.82 million euros, Woods donned the famous green jacket of the winner for the fifth time in front of his mother Kultida, daughter Sam and son, Charlie.
"It has come full circle," Woods said. "This tournament has meant so much to me and to have everyone here means so much to me and my family.
"Now to be the champion - 22 years since the first win is a long time. It's unreal for me to experience this. I just couldn't be more happy, more excited."
His first Masters title since 2005 moves Woods to within three of the all-time record of 18 majors won by Jack Nicklaus.
"A big well done from me to Tiger," Nicklaus tweeted. "I'm so happy for him and for the game of golf this is so fantastic."
Woods added: "I'm sure I will probably think about Jack's record going down the road. Right now it's a little soon. I'm just enjoying 15."