Reece Ludlow, 18, had picked up Yorkshirewoman Louisa Brannan, 35, a mother of three, only hours before in a pub in Mitcham, south London, and took her back to his nearby flat in Benhill Wood Road, Sutton.
They had sex but he then hit her over the head with a frying pan and stabbed her repeatedly with two knives.
Ludlow could not get over his break-up with his girlfriend Fon Promsan months before and called her when Miss Brannan was still alive.
He told her what he had done as Miss Brannan, originally from Springwood, in Huddersfield, cried out: ‘I’m dying’ in the background.
He later rang his girlfriend again to say she was dead, telling her “Come and help me, you will make it better, just come and see me, I only want to be with you, that’s all I want.”
Ludlow also telephoned his mother who alerted police early on March 14 last year.
He had admitted manslaughter but denied murder on the grounds of diminished responsibility.
Two doctors withdrew their support for Ludlow’s defence at Woolwich Crown Court and he then admitted murder.
Judge Nicholas Hilliard QC jailed Ludlow for life and ordered he serve at least 17 years.