8:47 AM PT -- Law enforcement sources tell TMZ a 49-year-old homeless man, Craig Tamanaha, was arrested. He was booked for criminal mischief, reckless endangerment, arson, disorderly conduct and criminal tampering.
Sources say the property damage totaled $500,000.
It's beginning to smell a lot like Christmas -- a very smoky one -- after someone torched the tree outside the FOX News building ... and cops already have a suspect in custody.
NYPD arrested a homeless man they believe acted alone in setting the 50-foot tree ablaze early Wednesday morning. No one was injured, and FDNY put out the fire pretty quickly, still ... we're told smoke filled the office building.
The tree had been decorated with 10,000 ornaments, and its 100,000 lights were just turned on Sunday during an on-air lighting ceremony.