Larry Merchant -- Floyd Mayweather and I Love Each Other Now!

Last year, they engaged in the best boxer-on-octogenarian fight ever ... but now legendary sportscaster Larry Merchant says he and Floyd Mayweather are "the best friends ever."

You'll remember ... Merchant and Mayweather really got into it during their post-fight interview last September ... when Merchant famously screamed, "I wish I was 50 years younger and I'd kick your a**."

But Sunday afternoon in Los Angeles, Merchant said he and Floyd buried the hatchet over the weekend in Las Vegas and each apologized for what went down.

As for Justin Bieber's appearance at the Mayweather-Cotto fight ... Merchant said he was "trying to get some face time on television. I think he needs it badly."