In an interview with The House magazine, John Penrose said the likes of Gibraltar and the Falkland Islands should also send MPs to represent them at Westminster.
The MP for Weston-super-Mare, who served under both David Cameron and Theresa May, said it would show that the UK was “committed to being a global nation post-Brexit”.
Britain has 14 Overseas Territories which are fully autonomous while remaining under the jurisdiction and sovereignty of the UK.
As well as Gibraltar and the Falklands, they also include Bermuda, the Cayman Islands, the British Virgin Islands and Montserrat.
Mr Penrose said: “What I am suggesting is they should be at least offered the chance to have an equivalent kind of devolution settlement that has already been agreed and negotiated with Scotland, with Wales and Northern Ireland.”.
The Overseas Territories would then become “equal elements” of the UK with the “same status” as Scotland, England, Wales and Northern Ireland, he continued.
“They would send MPs to the Westminster parliament here, they would have their own devolved governments like the Welsh Assembly or the Scottish Parliament, but it would just mean that it would be constitutionally stable, properly integrated, modern status for these overseas territories.
“It would show that we are committed to being a global nation post-Brexit.”
Mr Penrose argued the proposals would provide more “constitutional stability” surrounding the Overseas Territories, with the UK currently in dispute over Gibraltar with Spain and the Chagos Islands with Mauritius.
“Until we have a stable settlement, there is always going to be a risk of something blowing up,” he said.
The former Northern Ireland minister denied the move would be a return to Britain’s imperialist past.
He said: “People might make that argument but because we are offering and suggesting that these territories become equal parts of the United Kingdom, it’s hard to make an imperialist argument about this at all. It is clearly something that is talking about equal status.”
Mr Penrose said it would depend on the devolution settlement as to whether the Overseas Territories, such as the British Virgin Islands and the Cayman Islands, are subject to the same tax regime as the rest of the UK.
And he argued it would present opportunities for the Overseas Territories to export goods, such as lobsters from Tristan da Cunha, into the UK internal market with fewer restrictions.
“It just makes the trading ties and links between our respective parts of the UK a great deal simpler, a great deal more friction-free,” he said.
A spokesperson for the UK Overseas Territories Association says: “We are unaware of any formal consultation with the elected Governments of the UK Overseas Territories on this issue.”