This is the sequel to her 2019 book When We All Fall Asleep. Where Do We Go?. It addresses the pressures and issues of fame as well as those facing young women including sexual coercion.
Reviewers described the record as "defiant" despite its "muted tone".
The Guardian's Alexis Petridis gave the "universally great" album four stars.
Eilish said that on "possibly the most anticipated album 2021", she uses subdued but powerful song writing to reflect on how fame has permeated into every part of her life.
It is often exhausting to listen to a pop singer complaining about being a star. Eilish is a skilled song-writer, and it speaks volumes about her ability to make the topic feel genuinely affecting.
He wrote that this is partly because Eilish, despite her immense success, continues to express her fears through relatable intimacy, making her pop's antihero.
The album's title track has her wondering if her partners have seen her private confessions in interviews. My Future examines the stress of career progression versus personal relationships, while Your Power and Get Older deal with unwelcome sexual attention and consent for a MeToo generation demanding accountability.
Petridis felt that this authenticity sometimes removed her from the daily experience of her fans. "It's not worth pretending I'm still like them when I've sold millions of copies, sang a Bond theme, and appeared on Vogue's cover wearing a Gucci corset custom-made by me."
Eilish shared the album artwork in a long Instagram post.
Her trademark whispered vocal tone is still evident, but the album, which was recorded in lockdown with Finneas, her brother and collaborator, contains many clever production touches.
Petridis concludes that Happier Than Ever is "less immediately ear-grabbing than its predecessor... but the fact it's a higher-key album should not distract from its quality".
Similarly The Telegraph's Neil McCormick gave a four-star review, noting that the record contains "surprising musical twists and glittering barbs of lyrical empowerment".
He stated that "shimmering harmony" and "emotional travel" take listeners on an "emotional trip" that eventually casts "optimistic light" on Billie's dark night.
The subdued tone has caused some criticisms and fans to be dissatisfied with the absence of radio-friendly, bombastic singles.
In a five-star review of the new album, NME's El Hunt wrote, "Happier Than Ever fully establishes Billie Eilish as one of her generation's most significant pop artists - and, better still, does so without repeating a single trick from the debut that turned her life upside down."
Matthew Kent, the reviewer of The Line of Best Fit, lamented a lack of daring.
"The tempo never quite reaches fever pitch; instead Eilish is content with the tranquillity of tried and tested methods", he said, giving the album six out of 10.
Will Hodgkinson, the Times's editor, also stated that "there aren't any collaborations, no Elton Johns popping in for guest spots. Just Billie and Finneas doing one subdued song after another."
But his four-star review finishes by recognising "Happier Than Ever hits home because it has a core of authenticity and a dreamlike mood that intoxicates.
"Given the ease with which Eilish could have been diverted by now, this alone is an accomplishment."