The TV presenter and the Arctic Monkeys frontman have decided to end their four-year romance following a series of rows, but are hopeful of staying friends.
Her spokesperson said: "Sadly Alexa and Alex have split, although they remain close."
A source added: "They want to stay friends so it`s best to split now. They`ve been through a lot together and all their friends are sad they`ve called time as a couple.
"It was best that they both got out now and saved their friendship."
Insiders blame the pair`s working commitments for causing them to drift apart, and with Alexa, 27, based in New York for the summer while Alex is on the road with the band, the couple did not want to continue with a long-distance romance.
A source told the MailOnline website: "Alexa has moved all her stuff out and is concentrating on getting her American TV career back on track.
"Alex has gigs in America next month, but none of them are on the East Coast."
Cracks are said to have been appearing in the pair`s relationship for some time, with speculation their romance was in trouble surfacing earlier this month when Arctic Monkeys performed at the iTunes festival in London, which Alexa was hosting, yet the pair were not seen together at all during the evening, while they also barely socialised at the Glastonbury festival last month.
An insider told the Sunday Mirror newspaper: "Things haven`t been going well and they haven`t seemed like a couple for the past few weeks. At Glastonbury festival, they barely said a word to each other.
"Alexa was out seeing bands with all her buddies like Pixie Geldof and Fifi Brown, while Alex was on his tour bus chilling with his band. They really wanted to give it a go to hold it together and seemed to be getting back on track - but things got bad again and they both decided enough was enough."