The First Minister was reacting to the Prestonpans fighter’s victory over American Jose Ramirez in Las Vegas.
She tweeted: “Congratulations @JoshTaylorBoxer.”
Taylor became the first British fighter to claim the WBO, WBA, IBF and WBC titles simultaneously since the four-belt era officially began in 2004.
Known as The Tartan Tornado, he also received well-wishes from novelist and fellow Hibs fan Irvine Welsh, who wrote: “TTT! #No1.”
Las Vegas-based Scots actor Martin Compston was among those who paid tribute.
The Line of Duty star tweeted: “Sir Chris Hoy, Sir Andy Murray, tell me this man doesn’t deserve his place among them and not give a f*** at the same time.”
Taylor’s partner Danielle Murphy said: “Thank you so much to everyone for your well wishes and support!
“It honestly means the world to us! You are all the best.”