By Larry Fine

(Reuters) - Kris Bryant of the World Series champion Chicago Cubs capped off a dream season by winning the National League MVP award, while Mike Trout backed up his case as baseball's best by claiming AL honors for a second time.

The versatile, power-hitting Bryant, 24, was still in the afterglow of joining with his teammates to end the Cubs' 108-year wait for a World Series triumph with their seven-game victory over the Cleveland Indians.

"Obviously, I want to continue to get better and win more World Series. But it's all downhill from here," he joked on a conference call with reporters.

"This year has definitely been one of the best years of my life. Winning the World Series, now this is just icing on the cake."

After a unanimous victory in last year's Rookie of the Year vote, Bryant nearly duplicated the feat. He received 29 of the 30 first-place votes in romping to victory over Daniel Murphy of the Washington Nationals.

Bryant belted 39 homers and had 102 RBIs with a league-leading 121 runs scored, while hitting for a .292 average.

Before settling in as a Fall Classic fixture at third base, Bryant played 107 games at third, 69 in the outfield and manned first base nine times.

Los Angeles Angels outfielder Trout won his second AL Most Valuable Player award after first receiving it in 2014.

The 25-year-old Trout, who blends power, speed and defensive prowess, hit 29 home runs, drove in 100, scored a league-leading 123 runs, stole 30 bases and led the league with an on-base percentage of .441.

Trout received 19 first-place votes to nine for runner-up Mookie Betts of the AL East champion Boston Red Sox.

Despite playing for a Los Angeles team that finished fourth in the AL West at 74-88, Trout's outstanding season brought him recognition for a fifth successive campaign.

Trout finished second in the MVP voting in his 2012 rookie season, was runner-up again in 2013, won MLB's top honor in 2014 and was runner-up once more last year.

"It humbles you, it's an outstanding honor," Trout said in a conference call.

Trout is only the second MVP winner in either league to have won twice after finishing second in the previous election. The other was Barry Bonds in the National League in 1992 and 2001.

"I was very surprised," he said about winning. "It's an unbelievable feeling."

(Writing by Larry Fine in New York; Editing by Frank Pingue)