The 47-year-old Frenchman will sign a three-year contract with an option for a fourth season, and will officially take charge on July 6, ahead of the squad's return for pre-season training on July 10.
Sage arrives in south London on the back of an outstanding campaign with RC Lens, where he guided the club to a second-place finish in Ligue 1 and their first-ever Coupe de France title.
Lens finished just six points behind Paris Saint-Germain in the title race, with Sage named Ligue 1's manager of the year for his work transforming the club into genuine contenders.
According to reports from France, Crystal Palace had identified Sage as the ideal candidate to open a new chapter following Glasner's departure, and resisted competition from elsewhere for his signature.
That competition reportedly included a lucrative offer from Saudi Arabia, which Sage turned down in order to continue his career at the top level of European football.
Sage will not arrive alone. His trusted assistant Jamal Alioui has been confirmed as his deputy, while Damien Della Santa, a specialist in individual player development and set-piece situations, will also join the coaching staff.
Sandy Guichard, who spent a long spell at Monaco, completes the new arrivals and will take up the role of fitness coach.
Crystal Palace are set to confirm that existing coaches Paddy McCarthy and Andy Quy will remain part of the first-team setup, helping to ensure a smooth transition for the players.
According to ESPN, Crystal Palace will pay RC Lens a compensation fee of around €5 million for Sage, who still had two years remaining on his contract in France.
That figure could rise by a further €2 million in performance-related bonuses, including one guaranteed should Crystal Palace retain their Premier League status.
The move represents a significant financial step up for Sage, with reports in France suggesting his new salary will be close to four times what he earned at Lens, where his pay was in the region of €100,000 gross per month.
Before his rapid rise at Lens, Sage's senior managerial experience amounted to a single season at Lyon between 2024 and 2025, where he took the club from the bottom of the table into contention for European qualification.
Crystal Palace's primary target to replace Glasner had been Andoni Iraola, who instead opted to join Liverpool, leaving the door open for Sage to step into one of English football's most talked-about jobs following Palace's historic run of recent silverware.