Masisi hailed the 21-year-old sprinter as "Botswana's Sensation" after his outstanding performance on Thursday.
"Botswana's finest sporting moment," beamed the Mmegi newspaper after Tebogo produced a stunning run in the 200m to take gold, leaving pre-race favourite Noah Lyles trailing in third.
To add to his performance, he also set an African record of 19.46sec.
Tebogo's achievement will be "etched in the annals of the history of the republic", the president said.
The Olympic medal is Botswana's third after Nijel Amos won silver in the 800m at the 2012 London Games and the men's 4x400m relay team took bronze in Tokyo in 2020.
Videos shared on social media showed students at the University of Botswana dancing and singing into the night, while people across the southern African nation posted their pride on X and Facebook.
"History made!" Masisi said on his X account. "My voice is completely gone thanks to the phenomenal #LetsileTebogo."
Masisi also paid tribute to Tebogo's mother, his greatest fan, who died in May.
Tebogo is only the second athlete from Africa to win a medal in the 200m and the first ever to take gold.
Namibian Frankie Fredericks won silver in Barcelona in 1992 and Atlanta in 1996.
Botswana National Olympic Committee senior vice president Tshepo Sitale told AFP that the committee was "happy beyond measure" about Tebogo's achievement.
"Letsile is a rare talent and he has put Botswana on the map," he said, adding that the sprinter would be welcomed home next week with a ceremony at the airport and a motorcade.
"Welcome to the club, Letsile Tebogo!" silver-medal winner Amos said on Facebook. "Your achievement is not just a personal triumph; it's a monumental moment for our nation, especially after over a decade without an Olympic medal."
