Jota's Liverpool team-mate Darwin Nunez said there were "no words of comfort for so much pain".
"I will always remember you with your smile, as a good companion on and off the field," he said.
"I send all my strength to his family, from where he is I'm sure he will always be with you, especially his wife and three children."
Former Liverpool and England defender Jamie Carragher said he was "in a state of shock".
"I can only imagine how his team-mates feel at Liverpool and Portugal, they must be in a world of pain with his friends and family," Carragher told Sky Sports.
"It just shows us all how quickly life can change. What a summer he's had, and you get this devastating news that his family have had in the last few hours. You can't even comprehend it."
Former Liverpool and England midfielder Steven Gerrard posted on Instagram: "RIP Diogo. Condolences to his family and friends during this incredibly sad time."
Jota's Portugal team-mate Ruben Neves, who is playing at the Fifa Club World Cup for Al-Hilal, said: "They say we only lose people when we forget them. I will never forget you."
Fulham striker Raul Jimenez, who played with Jota at Wolves, posted on Instagram: "It's hard to get this kind of news and I still can't believe it.
"An excellent colleague, friend and above all a great father. Thank you for everything friend, we will always remember you."
NBA legend and LA Lakers power forward LeBron James, who is a minority owner of Liverpool, wrote on X "my prayers go out to his loved ones".
Legendary tennis player Rafael Nadal described Jota's death as "sad and painful news".
"All my love, affection and support go out to his wife, children, family and friends at this difficult time," the 22-time Grand Slam champion said.
Manchester City's Jack Grealish posted he was "lost for words" while Manchester United's Portuguese defender Diogo Dalot said he is "speechless".