The move represents the first major piece of business under manager Michael Carrick, who took charge on a full-time basis after guiding Manchester United to a strong finish to the season.
Carrick has made strengthening central midfield his priority for the upcoming transfer window. United have agreed a deal worth €40.5m, which could rise to €45m with performance-related add-ons.
In sterling terms, that equates to an initial £34m plus a further £3.8m in potential bonuses. Ederson, 26, has agreed to a four-year contract with the option of a fifth season, a structure that could keep him at Old Trafford until 2031.
The move has been delayed by the Brazilian midfielder's involvement at the World Cup. Ederson was a late call-up to Carlo Ancelotti's squad after right-back Wesley suffered a thigh injury in a pre-tournament friendly against Egypt.
Brazil opened their World Cup campaign against Morocco, drawing 1-1, with Ederson having linked up with the squad in the United States in the days before the tournament.
His arrival at United is expected to be confirmed once the formalities of the medical are completed, with the transfer not due to be finalised until the early part of next month.
Ederson joined Atalanta from Salernitana in 2022 and has made well over 150 appearances for the Bergamo club.
He becomes United's first signing of the Carrick era, brought in to address a midfield that is losing experience this summer.
Casemiro is leaving Old Trafford at the end of the month after four years with the club. His departure, combined with question marks over Manuel Ugarte's long-term future, has left Carrick short of options in the engine room.
United are not expected to stop at Ederson.
The club are also working on deals for a new left-back and a left-winger, with Lewis Hall and Bradley Barcola among the names under consideration for the left-hand side.
A second central midfielder remains a target as well, with West Ham's Mateus Fernandes attracting genuine interest from Old Trafford.
For Carrick, the early movement on Ederson sends a signal about the pace at which he wants to operate this summer.
Having inherited a squad short of legs and intensity in midfield, his first signing addresses exactly that gap.
Ederson's profile, an athletic, pressing midfielder shaped by Gian Piero Gasperini's demanding system at Atalanta, fits the kind of energy United have lacked since Casemiro's powers began to wane.
Whether he can adapt quickly enough to make an instant impact may decide how the rest of Carrick's rebuild is judged.