The Ligue 1 club confirmed the Frenchman's arrival on a five-year contract on Wednesday via their official Twitter account.
Per Goal's Tom Maston, Monaco paid his €40 million (£37.1 million) buyout clause to secure his services.
However, despite selling Romelu Lukaku to Inter Milan, the Premier League's transfer deadline passed last Thursday without the Red Devils having brought in Ben Yedder or another forward to replace the Belgian.
The 29-year-old was a prolific goalscorer for Sevilla:
Eleven Sports shared his highlights with the Spanish club:
He spent three strong seasons with Sevilla, the most recent of which was his most productive. Ben Yedder bagged 30 goals in all competitions in the 2018-19 campaign, along with 11 assists.
As football statistician Dave O'Brien demonstrated, he offered plenty against Sevilla's toughest opponents:
Football reporter Lee Roden was an admirer:
Monaco finished 17th in Ligue 1 last season, avoiding the relegation play-offs by just two points.
They scored just 38 goals, too, so Ben Yedder's arrival should make them much more potent in the final third and improve their prospects of avoiding a relegation battle this season.
As for United, with no replacement for Lukaku they'll be relying on Marcus Rashford and Anthony Martial to lead the line.