HMS Southampton is due to leave Portsmouth Naval Base on Friday afternoon to be towed to a scapyard in Turkey.
The decommissioned Type 42 destroyer was sold along with HMS Exeter and HMS Nottingham to Leyal Ship Recycling last month.
Nottingham is due to leave next Tuesday.
Exeter, which was one of the last remaining ships to fight in the Falklands War, was towed to Leyal’s scrapyard on September 22.
The dates and timings of Southampton’s and Nottingham’s departures are dependent on the weather as the ocean-going tugs need a clear run to get to Turkey, the Royal Navy said.
The navy advises people who wish to see the ships leave to check the shipping movements – which are published in The News every day.
Southampton, which was built by Vosper Thornycroft in Southampton, was commissioned in 1981 and decommissioned in 2009.
Nottingham was commissioned in 1983.
She was mothballed in 2008 and decommissioned in February last year.
The three ships have a combined scrap value of around £2m.
But the sale price is not being disclosed by the Ministry of Defence.