Galaxy have confirmed a deal is in place which will see the 33-year-old move to the San Siro for three months from January.
The switch will allow Beckham to play competitive games during the Major League Soccer close season and keep in with England manager Fabio Capello.
But Galaxy boss Bruce Arena has been left furious with the disruption inflicted on his own pre-season plans.
He said: "On the surface, it sounds like an odd proposition.
“I don’t see where that benefits MLS or the Galaxy. I don’t know if there’s anything true in the rumour.
"I would think given the position the Galaxy is in and the fact that we’re rebuilding our team and trying to have a successful year, it would seem very odd to me if we were loaning out our top players at the start of the season.
“It would seem pretty odd to me to operate that way.”