The 23-year-old will become a Red Devils player once the Borussia Dortmund midfielder has completed a medical and obtained a UK work permit, with the move expected to be finalised by the end of June.
Kagawa, who has scored 11 goals in 33 caps for Japan, admitted there were other clubs interested in the midfielder but he wanted to move to the 19-time English champions.
“Well a few teams had offered,” said Kagawa.
“But Manchester United were the first to give me a formal offer, after that, in the process of talking with various teams, it was Manchester United I felt I would like to join the most.
“I have not completed the contract, and I have not had a medical check or signed the document, although having said that, we have almost come to an agreement.
“Now that the opportunity to join such a big team like Manchester United has come, and of course I had some worries about the type and quality of the players, with the style of football there.
“I took many things into consideration, but in the end I found a strong desire to challenge myself at United.”
Dortmind signed Kagawa from Cerezo Osaka for €350,000 (£284,000) in 2010, and the attacking midfielder scored 29 goals in 71 appearances for Jürgen Klopp’s side as they won back-to-back Bundesliga titles.
“Of course, I would like to play in the hole, that is my best position,” he added.
“I would like to build my own status there, and earn trust in that position.
“It is true that this will be my big challenge, I must not make any mistakes, and to not make any mistakes, I think I need to make much more effort than ever before.”
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