Garcia wins first WTA title since 2019 in Bad Homburg
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It was the 28-year-old French player's eighth career title and her first since Nottingham in 2019.
The former world number four dropped the opening set as the Canadian Andreescu edged a tiebreak.
Garcia came back though to break twice in the second set before clinching the match in a third set when both players struggled to hold their service.
Garcia will face British-Japanese world number 206 Yuriko Miyazaki in the opening round at Wimbledon while Andreescu faces American qualifier Emina Bektas.