Marvel's Avengers is not canon according to Digital Spy, who recently spoke to the game's studio creative director, Noah Hughes. Or more specifically, it's set in a separate non-canon universe, and has zero connection to the Marvel Cinematic Universe, which is perhaps not very surprising when you consider the game's characters all feature unique and original designs different than the MCU's Avengers.
The bigger question is, how much or how little will it be connected to Marvel's Spider-Man? In other words, will it firmly establish a Marvel Interactive Universe? Well, all parties involved -- Crystal Dynamics, Square Enix, and Marvel Games -- have been a bit dodgy and unclear about this. So far the only connection revealed between the two is Taskmaster, who's in both games, and who seems to reference the events of Marvel's Avengers to Peter Parker in the PS4 game. Again, it seems to be one universe, but at the moment it's all a bit hazy.
According to Crystal Dynamics, Marvel's Avengers will be the start of the "Marvel's Avengers Universe," which sounds like its own separate thing. In other words, it seems to imply a Marvel Interactive Universe is off the table and the Taskmaster connection is nothing than a simple nod and wink.
As you will know, Marvel's Spider-Man has no relationship with the MCU either, but is canon to the comics, which have added Spider-Man PS4's White Spider suit.
That all said, Marvel Games has said in the past that games from its partners will not be forced to be canon, and even suggested they won't be combined into their own universe.
"We want to give [developers] freedom to tell their story and we want to make it an original story," said Marvel Games Creative Director Bill Rosemann back in 2017. "We want to give our partners freedom to look at all of Marvel history and to pick from what interests them. It's a bit like we're saying, 'Hey you're the chef, you're going to make this meal. Here's all of the ingredients. You pick the ingredients that you like and make a new meal.'"
"Marvel’s Avengers begins at A-Day, where Captain America, Iron Man, the Hulk, Black Widow, and Thor are unveiling a hi-tech Avengers Headquarters in San Francisco — including the reveal of their own helicarrier powered by an experimental energy source. The celebration turns deadly when a catastrophic accident results in massive devastation. Blamed for the tragedy, the Avengers disband. Five years later, with all Super Heroes outlawed and the world in peril, the only hope is to reassemble Earth’s Mightiest Heroes."