NEW YORK — Young rosters, small budgets, limited expectations.

No matter.

Bob Melvin of the Oakland Athletics and Washington’s Davey Johnson won big right away and were chosen as managers of the year Tuesday after guiding their teams to huge turnaround seasons.

Melvin beat out Baltimore’s Buck Showalter for the AL honor in a close vote by a Baseball Writers’ Association of America panel. In his first full season with Oakland, the rookie-laden A’s made a 20-game improvement, finished 94-68 and stunned just about everyone by winning the AL West with baseball’s lowest payroll.

Still, the unassuming skipper was surprised to win.

“Absolutely shocked. I mean, Buck had such a great year,” Melvin said.

Johnson was an easy choice for the NL prize after the Nationals — who had never enjoyed a winning season — posted the best record in the majors and made their first playoff appearance.

Johnson, who turns 70 in January, was honored for the second time. He was tabbed as the AL’s top manager in 1997, hours after he resigned from the Orioles in a feud with owner Peter Angelos.

This time, Johnson will get a while to enjoy the accolade.

The Nationals announced this month that he will guide them in 2013, when he will be the oldest manager in the majors. He’s set to leave the Washington dugout and become a team consultant in 2014.

“World Series or bust,” Johnson said on MLB Network. “It’s going to be my last year, anyway.”

Melvin also became a two-time winner, having been chosen in 2007 with Arizona. He and Johnson joined Jim Leyland, Bobby Cox, Tony La Russa and Lou Piniella as the only managers to win the award in both leagues.

La Russa was the only other Oakland manager to earn the honor, in 1988 and 1992.

Melvin received 16 first-place votes. Showalter got the other 12 after leading the wild-card Orioles to their first winning season since 1997, and Chicago White Sox first-year manager Robin Ventura finished third.

With five rookies in their starting rotation, the A’s were one of baseball’s biggest surprises this year — especially after trades, injuries and the suspension of veteran pitcher Bartolo Colon wreaked havoc with the roster. Oakland never panicked under Melvin’s cool demeanor, rallying from 13 games back on June 30 and overtaking Texas in the final week to win the division.