Troy Aikman -- Charters $10 MILLION Yacht ... To Branson's Private Island

Troy Aikman just took a baller vacation straight out of a Jay Z video ... chartering a $10 MILLION super yacht destined for Richard Branson's insane private island ... TMZ Sports has learned.

Sources tell us ... Aikman and his GF, Tracy Ripsin, boarded a PIMPED OUT yacht earlier this month called the Sea Legend ... an ultra-luxury ship with a gym, hot tub, pool, kitchen and all sorts of baller stuff.

We're told the couple set sail for Necker Island ... owned by Branson ... though it's unclear if Troy actually hung out with the billionaire or just kicked it his private paradise in the Virgin Islands.

It's good to be rich.