The chemicals - an entire stockpile of one type known as 'B precursors' and 44 tonnes of hydrochloric acid - arrived in Britain three weeks ago as part of international efforts to remove chemical weapons from the regime of president Bashar Assad.
Mr Ellwood said the work was an important step but warned there continued to be "credible reports" that industrial chemicals such as chlorine were still being used in the Syrian civil war.
The destroyed chemicals were part of Syria's weapons programme and could have been used to manufacture nerve agent.
The UK committed to handling the destruction of 15 per cent of Syria's stockpiles.
Work has now been completed at Ellesmere Port in a high-temperature incinerator operated by Veolio.
Mr Ellwood said: "By destroying these chemicals, the United Kingdom has played its part in the international effort to ensure that Assad's chemical weapons can never again be used against the Syrian people.
"The removal, and now the destruction in four countries, of the declared Syrian chemical stockpile show what can be achieved when the international community, including Russia, agrees to work together for the common good.
"The challenge remains to bring that same unity to bear in securing a political settlement to end this appalling conflict. Such a settlement is all the more urgent as the conflict continues to claim hundreds of lives each month."