The move comes as three former Type 22 frigates are set to be towed from Portsmouth Naval Base to the Leyal Ship Recycling centre in Turkey - the same scrapyard which bought the Ark Royal aircraft carrier. A fourth frigate is also to be taken to the Swansea Drydocks to be dismantled.
The Endurance's role as the Navy's Antarctic patrol vessel has been taken by HMS Protector - a former Norwegian research ship which was given a refit for its new role.
A MoD spokesman said: "HMS Endurance is due to go out of service in 2015 and, given the level of damage she sustained, it was not considered economically viable to repair her.
"The purchase of HMS Protector offers good value for money and secures the UK's long-term ice patrol survey capability."
The spokesman said the sale of the four frigates raised just under £3 million.