Ibrahimovic, whose contract was up at French champion Paris-Saint Germain, had long been linked with a move to Old Trafford and a reunion with his former manager Jose Mourinho.
In a tweet
he wrote: "Time to let the world know. My next destination is @ManUtd."
Ibrahimovic told CNN last year that he had turned down two approaches to move to England during his career from Arsenal and Manchester City.
The 34-year-old, who worked with Mourinho at Inter Milan, retired from international football after Sweden's exit from Euro 2016 earlier this month.
Manchester United has yet to confirm the move, but the forward is expected to have a medical on Friday before completing a deal.
It's a high-profile signing for United manager Mourinho, who replaced Louis van Gaal at the end of May.
Ibrahimovic has been effusive in his praise of Mourinho in the past and told CNN that he considered him a "mastermind."
United finished fifth in the Premier League last season -- 15 points adrift of surprise champion Leicester City -- and failed to qualify for the Champions League.
It did manage to win the FA Cup after defeating Crystal Palace 2-1 at Wembley.
Ibrahimovic will join the Premier League giant after a season in which he scored 38 league goals for PSG and 51 in all.
During his time in the French capital, he won 12 trophies in four seasons -- including the domestic quadruple on two occasions.
Ibrahimovic, who began his career with Swedish club Malmo, scored 62 goals in 116 games for his country before retiring earlier this month.
After making his debut for Malmo in 1999 he went on to play for Ajax, Juventus, Inter Milan, Barcelona and AC Milan before moving to Paris.
He has scored 392 goals in 677 during his club career and will now hope to add to that tally in England.
Ibrahimovic confirmed he would be leaving PSG in May while
also revealed he would return in a "managerial capacity" once his playing career had ended.
"I am very proud of the last four years," he told the club's website. "I loved every day I spent here. Paris Saint-Germain has become a star club in the world and I played a key role moving it forward.
"It is now the right time for me to take a different path. I would like to thank my teammates, the technical staff and all the people in the club. My heart is with the fans. They were amazing from the first day I came here. They are the best fans in France.
"It is not a farewell but only an au revoir. I came like a king, I leave like a legend but I will be back."
Ibrahimovic could make his United debut against Leicester City at Wembley in the Community Shield on Sunday August 7.
United's first league match takes place on Saturday August 13 away to Bournemouth.