Goldschmidt, 35, took home his first MVP honor, receiving 22 of 30 first-place votes and eight seconds for 380 points from a Baseball Writers' Association of America panel. Machado (seven first-place votes) was second with 291 points, and Arenado (one first-place vote) was third with 232 points.
It's the sixth time in Goldschmidt's 12-year career that he has finished in the top six in voting for the award. He is the fifth player to win his first career MVP at age 35 or older and the first since Dennis Eckersley in 1992.
"I think definitely as you age, you have to adapt, and that's some of what I've tried to do. I've tried to get ahead of it," Goldschmidt said in an interview on MLB Network. "You can't just try to do the same thing you did the year before. But yeah, kind of the stigma that as you get older, you're going to keep getting worse. I mean, nobody likes that. They don't like being told you can't do something, so it's definitely motivation.''
Goldschmidt led the NL in slugging (.578) and OPS (.981) while compiling the highest OPS-plus (180) of his career. Along with Arenado, he helped lead the Cardinals to an NL Central Division title.
For the season, he hit .317 with 35 home runs and 115 RBIs, ranking third in the NL in batting average, fifth in home runs and second in RBIs. Goldschmidt's sabermetric stats also ranked high, as he ranked first in WOBA (weighted on-base average), first in WRC+ (weighted runs created plus) and third in ISO (isolated power). He also ranked second in WAR among position players, just behind Arenado.
Goldschmidt's MVP was fueled by his first five months of the season, when he hit .332 with an OPS over 1.000. He slumped some in September, hitting just .245 with two home runs. He also went 0-for-7 in the Cardinals' wild-card loss to the Philadelphia Phillies.
Balloting was conducted before the postseason.
"Whether I won this or not, it was going to be a great year," Goldschmidt said. "This was my best year and the most fun I had, playing with Nolan and Albert [Pujols] and so many guys we had. So, it was just incredible."
Goldschmidt, a seven-time All-Star and four-time Gold Glove winner, was twice runner-up for NL MVP, in 2013 and 2015, and finished third in 2017. He was sixth last season.
"I never felt like I was missing something," he said. "I've had some great years."
Arenado, 31, finished in the top six in voting for the fifth time in his career after hitting .293 with 30 home runs. He also won his 10th consecutive Gold Glove award.
Machado, 30, carried the Padres to a wild-card berth after hitting 32 home runs while compiling a .898 OPS. With star shortstop Fernando Tatis missing the entire season due to an injury and then a suspension for PED use, and with newcomer Juan Soto struggling, Machado was the main source of offensive production for San Diego. According to ESPN Stats & Information research, he accounted for 20% of his team's home runs, third among NL players, while recording the highest percentage of his team's extra-base hits.
It's Machado's fourth time finishing in the top five in MVP voting, including twice with the Baltimore Orioles and now twice with the Padres.
Information from the Associated Press was used in this report.