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.
But she sued him in 2014, seeking to void their contract because, her lawyers claimed, he had "sexually, physically, verbally, and emotionally abused [Kesha] to the point where [she] nearly lost her life".
The allegations of abuse included two instances in which Kesha claimed Gottwald had drugged and raped her.
He denied the "false and shocking accusations" and counter-sued for defamation and breach of contract.
The bitter legal dispute has dragged on ever since. At every point, Kesha has either dropped her claims or lost in court, where matters of assault are difficult to prove.