It remains one of the indelible images of the 21st century.

On a frigid January morning in 2009, dozens of passengers found themselves perched on the wings of US Airways Flight 1549 — in the Hudson River.

Well. ON the Hudson River.

Just a few minutes after takeoff, the plane was struck by a flock of Canadian geese, rendering both engines powerless and necessitating a return to LaGuardia Airport — but when it was determined there wasn’t enough time to reach LaGuardia or any other nearby runway, the plane made an emergency crash landing on the water, and miraculously, all 155 passengers and crew survived.

At the helm of Flight 1549 was one Chesley “Sully” Sullenberger, who within 24 hours became one of the most famous American pilots this side of Charles Lindbergh.

It seems almost a foregone conclusion Clint Eastwood would direct and Tom Hanks would star in the movie version of the story. (Can you think of a better starting battery? I can’t.)

As accomplished as they are, it would be an understatement to say Eastwood and Hanks meet expectations. This isn’t just a solid piece of work; it’s resonant.

The 86-year-old Eastwood gives us an electrifying thriller, a wonderful in-depth character study and a fascinating airline safety procedural, while Hanks delivers another in a long line of memorable, nomination-worthy performances.

(Sidebar: How is it Tom Hanks hasn’t been nominated for an Oscar since 2001 with “Castaway”? Could it be the Academy has fallen into a pattern of taking his comfortable, outwardly effortless genius for granted?)

“Sully” begins with the immediate aftermath of the water landing, with Hanks’ Sully and his co-pilot, Jeff Skiles (Aaron Eckhart in one of his most measured and authentic performances), seemingly barely dried off being soaked in the icy waters of the Hudson when they have to face down a skeptical group of inquisitors from the National Transportation Safety Board, including Mike O’Malley as Charles Porter and Anna Gunn from “Breaking Bad” as Dr. Elizabeth Davis.

From the get-go, it’s clear some on the panel believe Sully might have panicked and actually had enough engine power and enough altitude and time to get back to an airport. They ask Sully questions about how much sleep he had before the flight, when he had his last drink — and if he was experiencing any problems at home.

They’re looking for chinks in the armor of a man who was already being hailed as a hero in the media and who seemed a bit uncomfortable under the lights, but didn’t say no to David Letterman or Katie Couric or plenty of other interview opportunities.

Eastwood directs with his usual economical style. (Even his longest-running films rarely seem to waste our time with overlong scenes of exposition, or unnecessary supporting characters.) We learn a little about Sully’s love of piloting and his resourcefulness in times of crisis via a couple of flashback scenes, and we’re introduced to a handful of flight attendants and rather thinly sketched passengers, including two adult sons and their beloved old pops, a young woman with a baby and a grown woman and her elderly mother.

Mostly, though, “Sully” is about Sully. Hanks is so good he could play this character in a one-man show with nothing but a chair and a telephone onstage and it would be riveting.

On the surface, Sully is a calm, cool, no-nonsense, self-effacing veteran of some 42 years as a pilot. But in the aftermath of the landing, he has visions of the plane smashing into Manhattan buildings, he has dreams of news reporters questioning his judgment, and he confesses his doubts and fears in intimate telephone conversations with his wife Lorraine (Laura Linney, who spends nearly every second of her screen time on the phone with Sully).

Eventually, at just the right time, “Sully” takes us through those harrowing, incredible 208 seconds when Flight 1549 is struck by those birds, and the engines burst into flames before dying out, and Sully and Skiles react in the cockpit, and the flight attendants repeatedly command, “Heads down, stay down, heads down, stay down!” and a commercial aircraft rapidly sinks in the skies above New York City (of all places) and eventually splashes down on the Hudson.

The editing and the special effects and the performances are so pitch-perfect, this is as close as you’d ever want to come to being on that flight on that January day.

“Sully” is an absolute triumph.

★★★★

Warner Bros. Pictures presents a film directed by Clint Eastwood and written by Todd Komarnicki, based on the book “Highest Duty” by Chesley “Sully” Sullenberger. Running time: 95 minutes. Rated PG-13 (for some peril and brief strong language). Opens Friday at local theaters.