The Star Trek Into Darkness
actress, 32, plans to marry U.K. financier Alex Cowper-Smith, her reps confirm to PEOPLE.
The pair first dated as teenagers while attending the Westminster School in London.
Later, Eve dated poet Adam O'Riordan – the pair met while both were college students at Oxford – but they eventually split in 2012, according to U.K. reports
Eve began her acting career in her native England and first gained fame among American audiences in the 2009 film Crossing Over
, starring alongside Harrison Ford
and Ashley Judd
She has also appeared in She's Out of My League
and Sex and the City 2
– as Charlotte York's intimidatingly sexy British nanny.
Reporting by JULIE JORDAN