The so-called ax murderer from Kalletal made a confession before the Detmold district court.
In a statement read by his lawyer on Monday, the 37-year-old described the act of June 18, 2022 at the start of the trial, in which out of jealousy he killed his former girlfriend's new boyfriend with an ax blow to the temple while he was sleeping.
The victim came from Lower Saxony.
The Azerbaijani denies the alleged rape of his ex-girlfriend.
The sex with the woman after the fact in an apartment in Kalletal in north-eastern North Rhine-Westphalia was consensual.
Both had met before the war in Ukraine.
The crime was followed by a week-long search and the accused fled in the direction of Poland.
The 37-year-old had served a prison sentence in Ukraine for a comparable act with an ax around ten years ago.
The district court is expected to announce a verdict in early February.