Gottwald sued Kesha in 2014, saying she had fabricated rape claims against him to get out of a recording contract.
In a ruling on Thursday, New York judge Jennifer Schecter said the star had defamed Gottwald when she texted Lady Gaga claiming he had raped Katy Perry.
Kesha was also told to pay interest of $373,671 (£289,000) on late royalties.
The pop star, whose full name is Kesha Rose Sebert, rose to fame in 2009 with Dr Luke-produced hits like Tik Tok and We R Who We R.