Steven Tyler -- Ok, Ok, I'm Engaged

The official word has finally come from Steven Tyler's famous giant lips -- even though we told you this last week ... he's engaged!

The giant rock girlfriend Erin Brady has been sporting lately is indeed an engagement ring -- and a worn-down rep for the "American Idol" judge confirms our story of 12/27 ... Tyler did indeed pop the question.

The whole situation has not sat well with Tyler's family. Sources close to Tyler have told us they are peeved they only got wind on the engagement AFTER he proposed.

The couple has been together since 2006.