Negotiations have been on-going with the Japan international for a number of weeks.
The deal is subject to a medical and work permit, although this is thought to be a formality.
Kagawa is currently on international duty and played in Japan's 3-0 World Cup qualifying round victory over Oman at the weekend.
"The deal is subject only to the player medical and obtaining a UK work permit. These conditions are anticipated to be completed by the end of June.
"Further details will be announced in due course."