Williams, 37, did not cope with the 19-year-old’s quality in a 6-3 7-5 loss.
Canadian 15th seed Andreescu, in the main draw here for the first time, blew a double break in the second set before taking her third match point and falling to the ground in disbelief.
“This year has been a dream come true,” Andreescu told the crowd.
“I am beyond grateful and truly blessed. I’ve worked really hard for this moment. To play on this stage against Serena – a true legend of the sport – is amazing.”
To the disappointment of a stunned home crowd on a passionate Arthur Ashe Stadium, Williams has now lost four successive major finals.
“Bianca played an unbelievable match,” Williams said. “I’m so proud and happy for you, it was incredible tennis out there.”
Williams, seeded eighth, looked edgy throughout as she aimed to match Australian Margaret Court’s tally of all-time major wins, handing over the first three of Andreescu’s five breaks of serve with double faults.
By contrast, Andreescu played with the confidence which has marked her out as a star in a stunning breakthrough year.
She is the first Canadian to win a tennis major and the first teenager to win a Grand Slam since Maria Sharapova claimed the 2006 title at Flushing Meadows.
She is the first teenager to win their maiden Slam since Russian Sharapova at Wimbledon in 2004.
Andreescu kept her nerve to take a third match point with a forehand down the line, dropping her racquet to the ground and then, after a warm hug with Williams, lying on the court with her arms spread out as she contemplated her achievement.
After returning to her feet, she used a hastily-arranged step ladder to climb into her player’s box and embrace her nearest and dearest, including parents Nicu and Maria.
Andreescu blocks out crowd to complete remarkable year
Before the match, Andreescu said if someone told her 12 months ago she would be facing Williams in the US Open final she would have thought they were “crazy”.
Tellingly, in a sign of her unwavering confidence, she said she would not have felt the same if they told her the same thing a fortnight ago.
Twelve months ago she lost in the first round of qualifying at Flushing Meadows and was ranked outside the top 200 in the world.
But she has become the most talked-about young player on the planet following a remarkable rise this year.
Andreescu, whose Romanian parents Nicu and Maria emigrated to Canada in the 1990s, had only played six tour-level matches at the turn of the year.
Since then she has won prestigious WTA Premier titles at Indian Wells and Toronto, rising to 15th in the world as a result and raking in £1.79m of her £1.97m career prize money.
Now she will climb to fifth in the world and take home another $3.85m (£3.13m) after this success.
Andreescu was fearless throughout her maiden Grand Slam final and unfazed by the occasion of playing an American icon on the biggest tennis court in the world.
Although the crowd was unsurprisingly backing Williams throughout inside an incredible noisy Ashe, the manner in which Andreescu coped and reset after seeing her double break in the second set disappear was remarkable.
At one point, Andreescu even put her fingers in her ears as the volume became particularly loud as Williams fought back from 5-1 down.
After her first Championship point went begging in the seventh game, another disappeared when Williams hit an ace for 30-40 in what proved to be the final game before Andreescu sealed victory at the third attempt with a forehand winner.
“I definitely had to overcome the crowd. I knew you guys wanted Serena to win,” a smiling Andreescu said in her on-court victory speech.
“Obviously it was expected for Serena to fight back, but I tried my best to block everything out. I’m glad how I managed to do that.”