Tekashi 6ix9ine should be sleeping a little easier tonight 'cause cops say they have the three men who beat the crap out of him in custody!

A rep for the Palm Beach Sheriff Office tells TMZ ... detectives rounded up Rafael Medina, Jr., Octavious Medina and Anthony Maldonado for assaulting and robbing the New York rapper. The suspects were being booked Thursday evening and processed into county jail.

TMZ broke the story ... three men assaulted the rapper earlier this month while he was in the sauna at an LA Fitness in South Florida. Surveillance video showed them make a beeline for him as soon as they entered the gym.

It's unclear if the suspects have any connection with the gang members Tekashi flipped on in federal court.

Despite the threat of retaliation after he testified, 6ix9ine hardly went into hiding once he finished his abbreviated prison sentence. He returned to making music and trolling his enemies on social media.

Even after the gym attack, he claimed he wouldn't increase his security because he saw the incident as a fluke.

It will be interesting to see if he returns to his regular gym routine now that his alleged attackers are behind bars.