The Russian won 6-3, 6-2 to lift her first crown at one of the four Grand Slam tournament venues in Melbourne, Paris,London and New York.
Both women, who were playing in their first final at a Grand Slam tournament, started tentatively.
Neither was able to win their first two service games to leave the score all-square at 2-2 after 22 minutes.
Chwalinska finally held to lead 3-2. But that was as good as it got for the 24-year-old Pole over the next 45 minutes.
Andreeva reeled off the next nine games to take the opening set 6-3 and rack up a 5-0 lead in the second set. Maja Chwalinska came through three games in the French Opening qualifying tournament to reach the main draw.
Chwalinska at least stopped the rot to get on the board and prolong proceedings on centre court at Roland Garros.
And Andreeva added a touch of drama.
At 5-1 up and serving for the title, she botched her first chance to claim the spoils.
Serving to stay in the match at 2-5 down, Chwalinska faltered again.
Andreeva fell to her knees after slapping away the backhand winner that brought her the title after 81 minutes.
After being handed the Coupe Suzanne Lenglen by the former champion Mary Pierce, Andreeva held the trophy aloft to soak up the adulation.
"It's very special for me personally," she said during the award ceremony. "I was watching the French Open on TV when I was very young and it's been a big dream of mine to win this tournament," she added.
She will collect a winner's cheque of €2.8 million.
Andreeva forgets the plan to stun Sabalenka and reach French Open semi-final
Rise to the top
Chwalinska, who came into the main draw of the French Open at 114 in the WTA rankings, will rise into the top 30 on the back of her surge from the qualifying tournament which started on 18 May to one of the most prestigious finals on the international circuit.
"Congratulations to you Mirra," said Chwalinska after receiving her runner-up medal.
"You're an incredible player. Young and talented ... it's so annoying!
"I really felt I tried my best. I definitely will not forget these three weeks. Paris will stay in my heart."
On Sunday, the men's singles final pits the second seed Alexander Zverev from Germany against the 10th seed Flavio Cobolli from Italy.
Neither player has won a Grand Slam tournament. However, Zverev will go into the showdown on centre court as favourite.
The 29-year-old has played in three Grand Slam tournament finals while Cobolli, 24, will appear for the first time in a major final.


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