Andreeva powered to a 7-5, 6-3 victory in a hard-fought duel in Indian Wells to complete a superb week in California.
Reigning French Open champion Andreeva, 19, clinched the title without dropping a set in the tournament.
She is only the third teenager after Chris Evert and Maria Sharapova to win the WTA Finals on their debut.
"It feels amazing, of course I'm super-privileged to put my name in that group," said Andreeva.
The teenager thanked friends, family and support staff in a victory speech, before light-heartedly thanking herself for her success.
"I want to thank myself for always doing the hard work, for never quitting, for always believing in myself, for not taking the days off, for working every day, and for committing to what I have to do," said Andreeva, wearing a track-suit top with the slogan "I want to thank myself."
A gruelling 1-hour 48-minute duel saw Andreeva secure a break in the opening game of the first set before holding for a 2-0 lead.
Ukrainian veteran Svitolina broke back in the fourth game, conjuring a sublime angled volley to level at 2-2.
Svitolina was soon back under pressure though, conceding another break to go 4-3 down before Andreeva held for a 5-3 lead.
There was more drama to follow when Andreeva served for the first set at 5-4 up.
She opened with back-to-back double faults to go 0-30 down, and then yanked a wild forehand wide to give Svitolina two break points at 15-40.
A long forehand gave Svitolina the break to knot it at 5-5 but Andreeva hit back immediately with her third break of serve to regain the advantage at 6-5.
The Russian made no mistake when serving for the set for a second time, holding comfortably to go 1-0 up.
The second set followed a familiar pattern, with both players trading some brutal groundstrokes in a series of long rallies.
Andreeva broke to take the lead at 1-0 but Svitolina responded in a marathon second game, breaking back after converting her seventh break point to level at 1-1.
Andreeva edged back in front with a break to go 3-2 up and then held for a 4-2 lead.
The next two games went with serve to leave Svitolina serving to stay in the match at 5-3 down.
A fortunate net cord left Andreeva with three match points at 0-40.
Svitolina saved the first and looked poised to save another, only to hit a wide open overhead smash into the net to give Andreeva the win.
Svitolina, who had been thumped 6-4, 6-0 by Andreeva in the opening round-robin game of the tournament, took positives from her performance.
"After the first match I was not expecting to play in the final," Svitolina said. "Unfortunately it didn't go my way but I gave it my all."