Earlier this month, Posey singled off Feliz as the Giants beat Texas in the clinching Game 5 of the World Series.
"It's hard to believe it's been two weeks," Posey said.
Posey hit several key home runs and helped the Giants win the crown for the first time since 1954. He easily outdistanced Atlanta outfielder Jason Heyward for the National League award.
Feliz, the rocket-armed righty who set a rookie record with 40 saves as Texas reached its first World Series, finished far ahead of Detroit center fielder Austin Jackson for the AL honor.
"I hope it's not a fluke. I hope I have a better season next year," the 22-year-old Dominican reliever said through a translator on a conference call.
Promoted from Triple-A on May 29, Posey quickly adjusted to the big leagues — both at the plate and behind it.
The 23-year-old Posey hit .305 with 18 home runs and 67 RBIs. He homered eight times after Sept. 1 in leading the Giants to the NL West title, and his homer on the final day of the regular season helped them clinch the division.
Posey was picked first on 20 of 32 ballots in voting by members of the Baseball Writers' Association of America. Voting was done by two members of the BBWAA in every league city after the regular season, with each person listing three players.
Posey was left off the ballot by Yasushi Kikuchi of Kyodo News from the Los Angeles-Anaheim chapter. Kikuchi chose Florida first baseman Gaby Sanchez first, Heyward second and St. Louis pitcher Jaime Garcia third.
"I think Rookie of the Year is for the rookie player who plays better than any other through the entire season. From this standpoint, Gaby and Jason produced more hits and played more games than Posey. Also, Jaime Garcia pitched as a starter through the entire season," Kikuchi said in an e-mail to The Associated Press.
Born Gerald Dempsey Posey III, the nickname "Buster" runs in his family. He was driving with his wife to the Florida Keys when he got word that he had won. He acknowledged he was wondering about the outcome.
"I think I'd be lying to you if I said I didn't think about it," he said on a conference call.
Feliz got 20 first-place votes and was listed on all 28 ballots. He drew seven seconds and one third. He was at Rangers Ballpark, where the World Series ended, when he found out he'd won.
The NL Cy Young will be the next major award to be announced. Philadelphia ace Roy Halladay is considered the front-runner for Tuesday.
Posey hit third and even cleanup for the Giants as they brought the championship to San Francisco for the first time. He was equally praised for handling a pitching staff that seemed to get better throughout the postseason.
Posey became the first Rookie of the Year winner to become a World Series champion in the same season since Boston's Dustin Pedroia in 2007. The last NL player to do it was Florida's Dontrelle Willis in 2003.
A star at Florida State, the Georgia native went to see the Seminoles play Clemson last weekend. Several football fans in the crowd recognized one of baseball's fastest-rising stars.
"That was nice," he said.
Posey played briefly at first base when he was called up, then moved to catcher when the Giants traded Bengie Molina to Texas. He had a 21-game hitting streak in July.
Posey finished with 129 points in the rookie voting. Heyward, who hit .277 with 18 home runs and 72 RBIs, got nine first-place ballots and 107 points.
Garcia drew one first-place vote and 24 points. Sanchez got the other two first-place votes and had 18 points.
Posey was the sixth Giants player to win the honor that was first awarded to Jackie Robinson in 1947. Willie Mays, Orlando Cepeda, Willie McCovey, Gary Matthews and John Montefusco also won. Montefusco was the most recent, in 1975.
Six catchers have won in the NL, with the Cubs' Geovany Soto the most recent in 2008.
Feliz went 4-3 with a 2.73 ERA in 59 games and finished with 122 points. He was a players' pick for the All-Star team this season.
Jackson, who hit .293, scored 103 runs and showed great range in center field, drew the other eight first-place votes and had 98 points. Minnesota third baseman Danny Valencia was third with 12 points.
Feliz didn't start the season as the Texas closer. Frank Francisco held that role, but lost the spot after blowing two early save chances and Feliz took over.
"At first, I didn't feel very comfortable," he said.
In fact, Feliz went to spring training trying to win a spot as a starter.
"I prepared as hard as I could to win a spot in the rotation. It didn't work out," he said.
For the Rangers, it all worked out more than fine.
Feliz went 40 for 43 on save chances and broke the rookie record of 37 saves set by 2000 AL Rookie of the Year Kazuhiro Sasaki of Seattle. Feliz later became the second-youngest pitcher to earn a save in the World Series, behind only Bob Welch.
This was the third time in the last six seasons that a closer won the AL award. Oakland's Andrew Bailey won last year and Huston Street of the A's got the award in 2005.
Feliz, who got a $10,000 bonus, became the second Texas player to win, joining Mike Hargrove from 1974.
Posey did not have a bonus provision in his contract.