A Dortmund crowd favourite during his 2010-12 stint at the Ruhr valley club, he helped them to win consecutive German league titles in 2011 and 2012 as well as the 2012 German Cup.
He left for United but failed to hold down a starting spot and was not part of new coach Louis van Gaal's plans for the season.
"Shinji Kagawa is highly skilled who sets the pace in a game," Dortmund CEO Hans-Joachim Watzke said.
"He really wanted to return to Borussia Dortmund and I am certain here at us he will find the peace, time and high regard which he needs to get back to his highest level after two years of irregular appearances."
Kagawa made 38 Premier League appearances for United, scoring six goals.
"I wanted to fulfil my dream of playing in the Premier League," Kagawa said.
"Now I am happy to be here at this great team, with this amazing environment and unique fans. Borussia is like a family and I am proud it did not forget me and that I am again part of it."
The creative 25-year-old joined Dortmund from Japan's second division for 300,000 euros (394,013.6 pounds) in 2010, playing 49 league games and scoring 21 goals despite missing half the 2010-11 season due to a fractured foot.
(Reporting by Karolos Grohmann, editing by Alan Baldwin)
Share
