Donovan had called Beckham a bad captain and portrayed him as stingy in an upcoming book.
Beckham practiced with the Galaxy on Tuesday for the first time since returning from a five-month loan to Italian club AC Milan.
Beckham says he spoke to Donovan recently, but the details of their conversation will remain private.
On Saturday at an MLS event, Beckham called Donovan's behavior "unprofessional."
Beckham plays his first game of the season with the Galaxy in New York at Giants Stadium on Thursday. On Sunday, the Galaxy face AC Milan in Carson.