With Galaxy currently on their winter break, Donovan, 26, will be with Bayern from January to March next year with Klinsmann hoping the United States forward can stay until the end of the season.
"Donovan made a very good impression during the ten days with us," explained Klinsmann, who knows the attacking midfielder from his time in California.
"We have agreed to sign the player on loan from January 1 2009 with an oral promise he will play in Europe until the season starts in the United States again."
Donovan is currently under contract with Galaxy until 2011 and will travel with Bayern to Dubai on January 1 for their winter training camp. "I need a fourth striker in the team and Landon will give us new possibilities in attack if someone is injured," said Klinsmann, referring to Luca Toni, Miroslav Klose and Lukas Podolski.
Last week, Donovan was named US football's Player of the Year for the fifth time, but struggled to impress on his last sojourn to the Bundesliga when he had a brief spell at Bayer Leverkusen.
Donovan has won 105 caps for his country and his market value is around €2.5 million ($3.1 million).