The 22-year-old arrives from RB Leipzig, where he enjoyed a prolific campaign last season, netting 21 goals and providing six assists.
Over the past two seasons, Sesko has scored more goals than any other player under the age of 23 in Europe's top five leagues, underlining his status as one of the continent's most exciting young forwards.
A full Slovenian international since 2021, Sesko made history as his nation's youngest-ever debutant. Since then, he has earned 41 caps and scored 16 goals, becoming a key figure for the national side.
Sesko's blend of pace, physicality and finishing ability made him a coveted target for several top clubs, but United have won the race for his signature.
His arrival is expected to add firepower to Ruben Amorim's attack as the club look to compete for major honours.
"The history of Manchester United is obviously very special but what really excites me is the future," said Sesko, via the club's official website.
"When we discussed the project, it was clear that everything is in place for this team to continue to grow and compete for the biggest trophies again soon.
"From the moment that I arrived, I could feel the positive energy and family environment that the club has created. It is clearly the perfect place to reach my maximum level and fulfil all of my ambitions.
"I cannot wait to start learning from Ruben [Amorim] and connecting with my team-mates to achieve the success that we all know we are capable of together."