The American was always in charge of the final, held over from Sunday due to poor weather earlier in the tournament.
Had it been played on Sunday, it would have meant the players contesting three matches in one day.
Oudin completed the victory over the former world number one in an hour and 35 minutes.
She broke early in the first set, only to be broken back; however she was to break again late in the set then served it out.
The 208th-ranked player dominated the second set against the 22nd-ranked Serbian.
Oudin has been given a wildcard for Wimbledon, which starts on June 25.
“This was a really great tournament for me and I’m definitely looking forward to coming back,” said the 20-year-old.
“I think it really helped me playing qualifying here, I played better and better each match. I love playing on grass.”
That certainly showed against Jankovic, who was looking for her first title in more than two years but has been back to her clean-hitting best this week.
Oudin’s forehand was particularly impressive and she combined that with a mix of power and slice off the backhand side.
“It was a great, great week for me and I definitely feel like I got better and better with each match,” she said.
Oudin announced herself as a star of the future in 2009 when she followed a fourth-round run at Wimbledon – where she beat Jankovic – with a quarter-final appearance at the US Open.
She has had some difficult times since and she came into the AEGON Classic ranked outside the top 200 but with the title, she will move up to around the 125 mark.
“I think I’m a lot more mature now and a lot smarter,” said Oudin. “I’ve learned a lot about the game of tennis, about my game and how I want to play, what I’m capable of. I’ve learned to play within myself, not try to do more than I can.”
For Jankovic, it was also a productive week, although she was disappointed to have missed out on a 13th career title.
“Overall I’m really pleased with the week. I had a lot of good matches here,” said the Serb after her 27th WTA singles final.
“I was happy to be competing and to be at this stage of the tournament. To be in the final is always great.
"Obviously I’m disappointed to lose in the final but at the same time it’s a good result for me right now. It’s just the beginning and it’s good for my confidence.”