World number 47 Ostapenko, who only turned 20 on Thursday, came from a set and 3-0 down to beat third seed Simona Halep on Saturday, incredibly securing her maiden WTA title in the process and becoming the first unseeded victor of the women's singles title in Paris since 1933.
The 20-year-old Ostapenko is the first unseeded woman to lift the Coupe Suzanne Lenglen since Britain's Margaret Scriven in 1933.
The Latvian, 20, hit 54 winners on her way to a "dream" 4-6 6-4 6-3 win over Romania's Simona Halep.
"I am upset but congratulations to Jelena, you are a great champion", said the Romanian, who would have taken the world number one spot with victory.
Halep marked herself out as a favourite for the title at Roland Garros after winning in Madrid and finishing runner-up in Rome, but a tumble in the Italian Open final left her with ankle ligament damage and cast doubt over whether she would play in Paris.
Ostapenko fired 54 winners and 54 unforced errors compared to Halep's eight and 10 respectively.
2017 - Before entering Roland Garros, she came close to winning three titles this year, losing in the semi-finals at Auckland and Prague and the final at Charleston.
If Halep wins, she also will move up to No. 1 in the rankings for the first time.
The Latvian ended the tournament with 299 winners - more than any other woman or man at the tournament.
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"I wasn't even thinking about it", she said. I'm just so happy.
But Halep, 25, said she felt sick to her stomach in the previous 24 hours leading up to the final as she tried, in vain, to get the enormity of the occasion out of her mind. "I think she's playing probably similar to my style, so she was my idol".
While Ostapenko flew in under the radar during this Grand Slam, that's an advantage she'll never hold again. It's her second grand slam final.
She trailed by a set and 3-0 but launched a memorable comeback with a remarkable display of fearless shotmaking. Also in the deciding moments, I played pretty well in those games.
Imagine her improved form at Wimbledon where that powerful hitting should suit her game.
But Ostapenko simply does not do fear and she continued to attack, slamming groundstroke winners on both sides, the power of her striking drawing gasps from the crowd.
"Actually, yeah, I think it's a quite bit deal in Latvia".
"I can not believe I am champion at 20 years old". She deserved to win. I was 3-1 down but I kept fighting.
"This one hurts a lot maybe because I am more - I realise more what is happening", said Halep, who will return to second in the rankings.