Ms Sturgeon added her name to the Rethink Trident statement, which has been organised by the Campaign for Nuclear Disarmament (CND) and Compass.
The statement says: “As Britain faces the deepest public spending cuts in living memory, the country can ill-afford to be spending in excess of £100 billion on replacing Trident with new nuclear weapons.
“Britain’s security needs are not met by nuclear weapons which can do nothing to combat the threats posed by terrorism, climate change or cyber warfare.”
Ms Sturgeon joins politicians including Labour leadership frontrunner Jeremy Corbyn and Plaid Cymru leader Leanne Wood in signing the statement.
Others opposed to Trident renewal include musician Annie Lennox, television personality Russell Brand and designer Vivienne Westwood.
Ms Sturgeon said: “I have opposed Trident and nuclear weapons for all of my political life - I even joined CND before becoming a member of the SNP.”