Darren Bridgeman, 34, from Malvern in Worcestershire, is wanted by US police for the murder of Tracey Bennawit and attempted murder of Adam Strickland.
Police in the US alerted Scotland Yard after the shootings on 24 June.
Mr Bridgeman handed himself in to police in Worcester. He is due before Bow Street magistrates on 13 July.
Prosecutors allege that on 24 June, Mr Bridgeman went to Ms Bennawit's home in Florida and shot her several times with a semi-automatic pistol before turning the weapon on Mr Strickland and shooting him in the chest.
'Semi-automatic weapon'
The following day, Mr Bridgeman was then said to have driven to Atlanta, Georgia, where he boarded a BA flight to Gatwick.
Seth Nevine, for the US government, told the court Mr Bridgeman handed himself in to Worcester police station by prior arrangement at 2120 BST on Thursday.
"On June 24, Mr Bridgeman attended the address of his ex-partner Tracy Bennawit. They had been in a relationship which was both a personal and business relationship.
"On the day in question, Mr Bridgeman attended the address armed with a semi-automatic weapon.
"Upon entering the premises, he shot Tracy Bennawit and, who was said to be her partner, Adam Strickland causing the death of Ms Bennawit and serious gunshot injuries to the chest of Mr Strickland," Mr Nevine said.
Mr Strickland identified Bridgeman as the gunman when questioned by investigators while in hospital in Orlando, said the prosecutor.
Mr Bridgeman moved to the US on a student visa in 1991, the court was told. He became a US citizen in 2001 and kept dual nationality.
Wearing a blue T-shirt and jeans, Mr Bridgeman spoke only to confirm his details and indicate that he would not consent to extradition to the US. He was remanded in custody.
Miss Bennawit's 14-year-old son managed to escape uninjured from the scene in Oviedo, Seminole County.
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