Babe Ruth -- Legendary 'I'll Knock a Homer for You' Ball ... SOLD at Auction For $250K

Babe Ruth's most famous signed ball -- and possibly the most storied artifact in baseball history -- just sold for a whopping $250,642 at an online auction tonight ... TMZ Sports has learned.

Here's the story -- Babe gifted the ball to a seriously ill little boy named Johnny Sylvester during the 1926 World Series ... inscribed with the promise "I'll knock a homer for Wednesday's game."

Sure enough ... the Bambino blasted three homers that Wednesday against the Cardinals in Game 4 of the World Series -- and miraculously, Little Johnny recovered from his potentially fatal illness.

88 years later the ball has a new home ... after Johnny Jr. -- who inherited the heirloom when his dad passed away in '90 ... decided to hock the thing for major cash at GreyFlannelauctions.com.

The auction house tells us, "We're very happy! It's a huge number!"

For a $250K price tag ... seems like a real home run.