The weekend take of the Disney and Marvel Studios' sequel should push it past the record held by James Cameron's epic of $2.7897bn (£2.23bn).
Marvel chief Kevin Feige hailed the achievement at Comic-Con in San Diego on Saturday, although it was still officially $500,000 short at the time.
Disney boss Alan Horn said fans had taken the film to "historic heights".
Avengers: Endgame has not just been a success at the box office, it has also drawn widespread critical acclaim. Reviews when it was released spawned descriptions such as "glorious", "irresistible", "intensely satisfying" and "masterful".
Its Rotten Tomatoes reviews are over 90%.
What are the numbers?
On Friday, Avengers: Endgame's global gross was $2.7892bn, half a million dollars short of Avatar, but its weekend take was always likely to push it through the barrier, as last weekend it raked in $2.8m across the world.
The figures are not adjusted for inflation and Avatar would still be ahead it they were.
Avengers: Endgame already had other achievements - including the biggest global opening of all time at $1.22bn when it was released in April, breaking the record of 2018's Avengers: Infinity War.
An Avengers: Endgame re-release with added footage at the end of June, and the recent release of Spider-Man: Far from Home, have helped give Endgame a box-office kick.
What's it all about?
Endgame is the 22nd offering in the Marvel Studios superhero franchise and the fourth in the blockbuster Avengers series.
Media captionWatch the Avengers: Endgame trailer
Film experts say fans embracing the Avengers characters has helped create a worldwide phenomenon.
We're not about to give away spoilers here - although by the looks of it there's no-one left who hasn't seen Endgame anyway.
Suffice it to say the Marvel Cinematic Universe (MCU) franchise began with Iron Man in 2008.
Most of the storylines in the Marvel movies since then have had objects called Infinity Stones playing a part and, well, it was up to the final movie to sort it all out, particularly as it had not gone well for the superheroes in the immediately previous movie, Infinity War.
Pats on the back from the bosses
Kevin Feige slipped out congratulations at Comic Con as he announced a bumper crop of 10 new superhero movies.
He admitted it would be "a matter of days" before Endgame became "the biggest film in history" and that "if you adjust for inflation, [James Cameron] still holds the title".
But he added to a large ovation: "But for right now today in Hall H, thanks to you, Avengers: Endgame is the biggest film of all time."
Alan Horn said in a statement: "Huge congratulations to the Marvel Studios and Walt Disney Studios teams, and thank you to the fans around the world who lifted Avengers: Endgame to these historic heights."
Actor Chris Hemsworth - aka Thor - said on Instagram: "Thank you to all the fans around the world that lifted Avengers Endgame to historic heights making it the top grossing film of all time!"
Oddly, Avatar is now also a Disney film, after Disney acquired much of 21st Century Fox in March.
Mr Horn said he looked forward "to the future of both the Marvel Cinematic Universe and Pandora (the Avatar milieu)".
Avatar 2 has a current release date of December 2021.