Fat Joe Says A-Rod Has His Blessing To Date J Lo

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Good news for A-Rod, Fat Joe isn't pissed he put the moves on Joe's "little sister," Jennifer Lopez ... telling TMZ Sports he's "all for" the brand new celebrity relationship.

Joe was in NYC promoting his new album when we asked him about the new twosome ... mainly if he thought the relationship was a good look for Jenny from the block.

If you didn't know ... Joe was DEVASTATED when J Lo divorced Marc Anthony, saying it was one of the "saddest days" of his life because both of them were like family to him.

Despite that, he told our guy he's A-OK with her dating A-Rod ... saying A-Rod is rich and successful, so it's a good look for J Lo.

Batter up.