The Czech 13th seed will play either top seeded American Serena Williams or Swiss 23rd seed Timea Bacsinszky in Saturday's final.
Safarova is the first Czech woman to reach the French Open final since Hana Mandlikova won the title in Paris in 1981. Prior to this year, her best showing had been a run into the last 16 in 2007 and 2014.
"It's a dream come true. I still cannot believe it," she said after converting her third match point.
Ivanovic, the champion at Roland Garros as a 20-year-old in 2008, had to battle hard to get into the last four, three times going the full distance.
In contrast Safarova had not dropped a set, winning five straight tie-breaks, one of those coming in the first set against defending champion Maria Sharapova in the round of 16.
But it was the Serb, watched by German World Cup winning footballer Bastian Schweinsteiger, who made the stronger start.
On the hottest day of the tournament so far, Safarova was close to going into an early meltdown as Ivanovic staggered her with some superb line drives.
The Czech player, making just her second appearance in a Grand Slam semi-final after last year's Wimbledon, knuckled down, however, to hold her next three serves and then redeemed her earlier loss with a break in the ninth game.
It was the turn of Ivanovic to struggle as Safarova won four games in a row and then served out for the first set to zero thanks to some dismal shot-making from the Serb.
The 13th seed was dominating the match now, with Ivanovic looking more and more out of sorts, and she had break points to go 4-1 up.
Ivanovic survived those, but her game was clearly off.
Safarova looked headed for a comfortable win, but inexplicably her serve collapsed at 5-4 and three double faults allowed Ivanovic to stay alive, finally converting a second break point after nine failures.
But it was only a stay of execution as Ivanovic failed to hold serve in the next game and Safarova this time made no mistake to record the biggest win of her career to date and book a place in the final.
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