"I feel incredibly excited," Kagawa told reporters at Tokyo's Haneda airport on Thursday before leaving for England.
"It's a new start and I feel re-energised. It's up to the players to get the results we need. I have a strong desire to do well."
Kagawa, an instant hit for United after being signed by Alex Ferguson from German Bundesliga side Borussia Dortmund in 2012, found himself largely frozen out last season under the troubled reign of David Moyes.
United's decision to sack the unpopular Scot in April, after just 10 months in charge, and the arrival of Dutch World Cup coach Van Gaal have left Kagawa sweating over his fate.
"I'll look more closely at my game and accept the challenge filled with passion," insisted the 25-year-old Kagawa, who gave three lacklustre displays at the World Cup as Japan finished bottom of their group.
Van Gaal is expected to decide quickly whether to offer Kagawa, who has two years left on his contract, an extended deal.
"It was the most disappointing experience of my life," Kagawa said of Japan's meek exit from Brazil. "How I can use that as a plus will depend on how hard I work."
Japan's World Cup flop triggered criticism of key players including Kagawa and playmaker Keisuke Honda after a 2-1 defeat by Ivory Coast, a goalless draw with 10-man Greece and a 4-1 thrashing by Colombia.
Manchester United will play in the pre-season International Champions Cup in North America beginning on July 24, with Japan team-mates Honda (AC Milan) and Yuto Nagatomo (Inter Milan) also taking part.
- Sports & Recreation
- Shinji Kagawa