A moving truck showed up Tuesday ... we're told to take Jordan Bratman's stuff away, and none too soon. We're told current BF Matt Rutler moved in weeks ago.
As one source connected with the threesome put it, "Thank God Jordan is moving out. It was getting really awkward, but Christina was letting Jordan stay for the sake of Max."
As TMZ first reported ... after Christina filed for divorce Jordan wouldn't move out of the house, so Christina was staying in various L.A. hotels, but eventually moved back into the family home.