Ibrahimovic posted a message on social media, accompanied by a picture of United's badge. It read: "Time to let the world know. My next destination is Manchester United. #iamcoming."
The 34-year-old will arrive on a free transfer following the expiry of his contact at Paris Saint-Germain, having won Ligue 1 four times in four years and scored 38 goals in 31 league games during his final season.
The Sweden international's move to the Premier League means he will be playing in the sixth different domestic league of his career, excluding only the Bundesliga of Europe's traditional top-five leagues.
He will now attempt to win a league title in a fifth major European league, under the guidance of Jose Mourinho, his former Inter Milan manager.
The pair's mutual admiration has long been a matter of record, and they share a common enemy in Pep Guardiola, who clashed with both during his time at Barcelona and will be in charge of United's cross-town rivals City next season.