Type 22s HMS Cumberland, HMS Campbeltown, HMS Chatham and HMS Cornwall are currently moored in Portsmouth Harbour.
The Ministry of Defence (MoD) expects to receive just under £3m from the sales agreed earlier this month.
HMS Cornwall has been sold to Swansea Drydocks while the other three have been bought by Turkish firm Leyal.
The two companies will recycle as many parts of the former Devonport-based ships as possible.
Aircraft carriers Ark Royal and Invincible have also been sold to the Leyal yard in recent years.
The four frigates were put up for sale in January with a preference for at least one of them to go to a UK ship recycler to determine the capacity of the UK's industry in the field.
An MoD spokesman said: "We believe this deal represents value for money and a number of tenders were received both nationally and internationally.
"Certain aspects of the ships' equipment will be recycled for use on other vessels and we have tried to be as economical with the disposal as possible."
Penny Mordaunt, Conservative MP for Portsmouth North, had hoped one of the frigates could have been sunk and turned into a diving attraction but bids in that field were rejected.
The ships are expected to leave Portsmouth in the autumn.
Four decommissioned Royal Navy frigates are destined for the scrapyard, the BBC has learned.