The 1998 and 1999 F1 world champion believes his countryman can emulate his success in the sport.
"I'm confident that he's going to have an unbelievable future ahead of him," Hakkinen told CNN World Sport.
"He's always been committing himself 100% to his dream of becoming world champion. What he achieved in Sochi yesterday shows that he has an unbelievable focus and concentration to succeed.
"I know what it feels like to win your first grand prix -- I'm so happy for Valtteri and I'm so happy to be part of his team. He's gonna win more races - just wait!"
Bottas' victory at Sunday's Russian Grand Prix
was his first in 81 grand prix starts and comes in his fourth race for new team Mercedes who he joined in January following the retirement of Nico Rosberg
Hakkinen, who is part of Bottas' management team, helped nurture the 27-year-old's talent from a young age -- and it didn't take him long to spot his talent.
"When I saw Valtteri first driving go-karts ... and when I went to see him testing in Formula 3 at Hockenheim I just needed to look one or two laps and I said: 'that's it, this guy is an incredible talent. This guy is a champion.'"
With a first win under his belt, Bottas has further spiced up what is developing into a memorable battle for the 2017 F1 Drivers' Championship.
The Finn is now third in the standings, 10 points behind teammate Lewis Hamilton and a further 23 adrift of championship leader, Ferrari's Sebastian Vettel.
But Bottas' Mercedes team face an uphill fight to stop a rejuvenated Ferrari
"At the moment the Ferrari is really consistent in qualification and in a race configuration," Hakkinen says.
"Mercedes is just quick for one lap but the long distance it's really lacking some performance. So they have to find a solution for that."
Valtteri Bottas is the 107th race winner in F1 history and the first new name since an 18-year-old Max Verstappen won the 2016 Spanish Grand Prix on his Red Bull debut.
It might have taken Bottas 81 races to cross the line first, but that record is still some way short of reigning F1 champion Nico Rosberg, who had to wait 111 races.
Mercedes remains the only constructor to win the Russian Grand Prix, but three drivers haven't been this close after the opening four races since the 2012 F1 World Championship. Sebastian Vettel went on to win that year with Red Bull.
Only eight Finnish drivers have ever raced in F1 and Bottas is now the fifth to record a race victory, following in the footsteps of Keke Rosberg, Mika Hakkinen, Kimi Raikkonen and Heikki Kovalainen.
Only France, Brazil, Germany and Great Britain boast better F1 pedigree than the icy Scandinavian nation.
"The Finnish mentality is good for Formula One," Bottas told CNN's F1 show The Circuit
"If you learn to drive here then everywhere else will not be a problem," he said. "Car control for people in Finland is pretty good because of the tricky conditions. You get used to it and I try to enjoy every single bit of it."
Sochi 2017 was the third time two Finns have stood upon the podium
, with Raikkonen and Kovalainen sharing the honor in Japan in 2007 and Hungary in 2008.
After leading FP1, eventual third-place finisher Raikkonen picked up the fastest lap of the race for the 45th time in his career, clocking one minute 36.844 seconds. Only Germany's Michael Schumacher (77) can boast more.