The cities were selected after Birmingham, Leeds, Newcastle, Sheffield and Manchester were removed from the list to host the music event in place of Ukraine.
Announcing the shortlist, Phil Harrold, the chairman of the BBC’s host city selection committee, said: “The Eurovision Song Contest is a very complex event and Liverpool and Glasgow have the strongest overall offer. We will continue our discussions with them to determine the eventual host city.
“We are determined to make the 2023 Eurovision Song Contest one that both reflects the winning position of Ukraine and is also an event that all of the UK can participate in.”
The decision sparked a flurry of excitement from key figures in Glasgow.
City council leader Susan Aitken said: “The competition has been very strong, but Glasgow has an unrivalled track-record for successfully hosting major global events.
“Between that experience and expertise; our famous live music scene, and one of the world’s top entertainment venues in the Ovo Hydro, Glasgow has everything it takes to host a show that the whole Eurovision family can be proud of.”
Culture minister Neil Gray added: “We are delighted that Glasgow has made the final selection to host the 2023 Eurovision Song Contest.
“The Scottish Government will continue to engage with Glasgow council as they progress their final bid.”
Further discussions will now take place with officials from Glasgow and Liverpool. The host city will be announced “within weeks”, the BBC have said, with the final decision a matter for the broadcaster in conjunction with the EBU.
Ukrainian entry Kalush Orchestra triumphed at the 2022 competition in Turin, Italy, but the European Broadcasting Union (EBU), which produces the annual event, decided the show could not be safely held in the country following Russia's invasion.
The UK was given the chance to host the event for the ninth time – more than any other country in the competition’s history – after Sam Ryder came second in the competition.
In August, a list narrowed down from 20 UK cities who initially submitted an "expression of interest" was released by the BBC.
Requirements included "a suitable venue and sufficient space to deliver the requirements of the song contest", necessary commitment to the contest including a financial contribution, and "alignment with the BBC's strategic priorities as a public service broadcaster".
First Minister Nicola Sturgeon previously voiced her support in June for Glasgow to become the home of the contest. The Ovo Hydro arena, which features in the Netflix film Eurovision Song Contest: The Story of Fire Saga, in had been previously rumoured to be a frontrunner.
Scottish Secretary Alister Jack said Glasgow had “got what it takes to go all the way”.
“Famous around the world for its brilliant music and welcoming spirit, with a track record in delivering global events, we know our biggest city would put on a fantastic show,” he said.
Scottish singer Lulu represented Britain at the Eurovision Song Contest in 1969, with song Boom Bang-A-Bang. She was the joint winner that year as she shared the prize with France, Netherlands and Spain with 18 points apiece.