Megan Fox & Brian Austin Green's New Home -- Bing Crosby's Former Pad

Megan Fox and Brian Austin Green are channeling a bit of old Hollywood ... paying top dollar for a house that once belonged to Bing Crosby, TMZ has learned.

Real estate sources at Trulia tell us Fox and Green dropped $3.35M for the 6,710 square foot ranch home -- which was originally a carriage house on Der Bingle's estate in Toluca Lake.

The place doesn't exactly inspire dreams of White Christmases ... the 4-bedroom, 6-bathroom crib underwent a contemporary makeover during an extensive 2008 remodel. It now has lots of exposed wood .. and the master BR has a 2nd story loft.