The 32-year-old musician-turned-actress split from her London-born lover in September, but the duo are said to have remained on good terms since they decided to call time on their relationship.
A source told Just Jared: ''Kat and Elyes broke up last month.
''It was an amicable split. They're still friends and work together almost everyday. They still love each other but just couldn't make things work.''
Katharine - who was the runner-up on the fifth season of 'American Idol' in 2006 - is currently starring alongside Elyes, 33, on the CBS drama 'Scorpion'.
Their relationship became public in 2014 when they were spotted kissing on the set of the show, which is based on the life of a computer expert.
Earlier this year, meanwhile, Katharine's divorce from Nicholas Cokas was officially finalised.
The actress and her ex - who married in 2008 - disagreed on the date they split, with Nicholas arguing it was May 2014, while Katherine claimed the split came in March 2013.
The judge reportedly agreed with Nicholas and as a result, he was awarded a bigger payout.
Katherine agreed to pay Nicholas spousal support, while he was also awarded 50 percent of income earned during their marriage, which included songs she worked on, her $700,000 contract with Columbia/Epic Records and income earned from her work on 'Smash', the musical drama series.
What's more, Katharine was ordered to pay him half of the money she earned for the pilot episode of 'Scorpion'.
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