Radwanska, who lost twice at the round-robin stage and upset Garbine Muguruza in the semis, came from a break down in the deciding set to win a tense final in two hours and five minutes.
The 26-year-old Pole, who was a last-minute qualifier for the eight-player season finale, was in floods of tears after winning the prestigious title at her seventh attempt.
“It just means everything — it was my first final and it couldn’t have been any better,” she said.
Radwanska dominated the first set but Kvitova hit back to win the second and take it to a decider at an increasingly tense Singapore Indoor Stadium.
The Pole went down a break early in the third but she snatched back control and saw off a gritty fightback by Kvitova, who was hampered by an injury to her heavily strapped right leg.