Garcia had a slow start, being dominated by Vekic in the first set where the French star lost her opening two serves and allowed her opponent to storm to a 6-2 win.
The tournament's top seed rallied back to take the second set after a tie-break win of 7-4.
The final set saw a hard-fought battle between the pair, with another thrilling tie-break to decide the match.
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Garcia took an early lead in the tie-break but eventually lost her serve to allow Vekic to level.
The 25-year-old raced ahead again to hold a 6-3 lead, but failed to take advantage of two match points before eventually securing the championship victory with an ace giving Garcia another 7-4 tie-break win.
The weather caused havoc throughout the week, with some earlier matches in the tournament moved indoors.
Garcia had her semi-final clash against Jennifer Brady suspended due to rain on Saturday evening, meaning the match had to be finished on Sunday morning which could have been the reason behind her sluggish start to the final.
The World No. 28 said "tennis is about passion and courage" as the Nottingham crowd gave her a standing ovation during the trophy ceremony.
Garcia admitted it was "tough to come back" after her semi-final session on Sunday morning and dedicated her win to her dad on Father's Day.
Second seed Vekic looked distraught after the match stating that she was "very, very sad" after losing but the 2017 Nottingham grass champion confirmed her wish to return to the tournament next season.
However, the 22-year-old praised the "amazing" crowd in Nottingham and the tournament organisers who battled with the troublesome weather conditions during the entire week.
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