"I'm really happy to win here", Ostapenko said after the match, evidently under the huge influence of emotions, "I think I still can not believe it because it was my dream and now it came true".
Her win makes her the youngest Roland Garros champion since Iva Majoli in 1997, and the youngest Slam victor since Maria Sharapova at the 2006 US Open. The last woman to win her first title at a major was Barbara Jordan at the 1979 Australian Open.
Those numbers are counter-balanced by her unforced errors - 54 on Saturday and 271 in total - but they were not enough to stop the energy-charged Ostapenko from bulldozing her way to the title, firing faster forehands on average than men's world number one Andy Murray.
The last player to lift the French Open as their first crown was Brazil's Gustavo Kuerten in 1997 - on the same day Ostapenko was born.
Ostapenko came back from 0-3 down in the second set to take control with some fearless groundstrokes during the two-hour contest.
The 20-year-old trailed by a set and was 3-0 down in the second to Halep - who would have become world number one with a win - but prevailed 4-6 6-4 6-3. The unseeded tennis player really believes now that "anything is possible".
"Of course I will probably now will have more pressure and attention, but I'm going to try to deal with that", she was quoted as saying by BBC Sport.
Ostapenko's wildness betrayed her as she served to stay in the set at 4-5, netting a forehand to offer Halep set point and drilling long to gift the Romanian the set.
At one point Saturday, it looked as if Simona Halep was on her way to her first ever major victory.
Ostapenko was hitting the ball so strong that her shots left Halep groggy.
"I'd like to say congratulations to Simona, you had a great week, you played great, I hope you have many more finals and you will win it", said Ostapenko, who was a first-round loser at the tournament in 2016.
Her daughter has taken her by surprise by winning a grand slam so early in her career, but she recalled how it was a triumph 10 years in the making. I have no words, it is my dream.
Again refusing to rein in her aggression, Ostapenko stormed through the final five games - seemingly breaking Halep at will.
Ostapenko's success owed much to an ultra-aggressive approach, which saw her rack up 54 winners in the final and would appear well-suited to the upcoming grass-court season.
"I will keep working, because I really want to repeat what I have done this tournament". "Maybe I wasn't ready to win it", she said. Also in the deciding moments, I played pretty well in those games. So I think from our perspective Simona can hold her head up high. "She kept Halep waiting on the baseline for almost a minute as she rearranged her towels and her bag at the start of the match". "She deserved to win", said the Romanina. I'm just so happy.
Back on the attack Ostapenko surged 4-3 ahead only for more errors to allow Halep to break back for 4-4.