Sammy Almahri pleaded guilty to murdering Nadine Aburas, 28, at the Future Inn on New Year's Eve 2014, before placing a "do not disturb" sign on the room door, South Wales Police said.
Almahri, 45, initially admitted manslaughter but denied murder, saying he was suffering from a mental disorder and carried out the killing after hearing the "voice of God".
He changed his plea to guilty during a hearing at Cardiff Crown Court.
In a statement, Ms Aburas' family said: "Justice has been done for Nadine.
"The right verdict has been returned. We wish to thank everyone who has assisted us throughout this tragic period in our lives.
"We ask now that we are given time to grieve and remember our beautiful girl."
Cardiff Crown Court heard the couple met on internet dating site MuslimMatch.com in 2013, after Almahri made the "fictitious" claim he worked for the FBI.
Almahri was described as being "besotted" with Ms Aburas and showered her with presents, including a car.
But the court heard the relationship soured the following year, when Ms Aburas visited Almahri in New York.
When she returned to Wales, the 28-year-old was described as looking "tired" and "drained".
She later contacted police saying she had been raped, although the complaint was not pursued by her or the police.
The court was told Almahri later threatened to post a naked photograph of Ms Aburas on Facebook and sent her a message just days before the death that said "you will be so sorry... I know your (sic) with someone else".
Almahri travelled to Cardiff on 29 December 2014 and was joined by Ms Aburas at the Future Inn hotel the next day.
Her body was found by a hotel worker at around midday on New Year's Eve.
After killing Ms Aburas, Almahri drove to Heathrow Airport using his victim's car and boarded a flight to Qatar.
The 45-year-old will be sentenced on 3 November, South Wales Police said.