Conservatives Philip Dunne, Daniel Kawczynski, Mark Pritchard, and Craig Williams all said they were delighted at the announcement of a deal.
North Shropshire MP Owen Paterson, also a Conservative and one of parliament's most long-standing and committed Brexiteers, said he hoped the agreement had delivered what people voted for, and that he would need to analyse the text of the agreement to decide whether it was a success.
Mr Dunne said: "This is a huge success for the Prime Minister, and a massive relief to the whole country. We will now be able to trade freely with the EU.
"I am particularly pleased for the British lamb and beef producers, who were facing significant disruption without an agreement.
"We have clearly got a difficult time ahead with Covid still rampant but the zero tariff, zero quota deal with the EU is just what everyone needs at Christmas to look forward to a brighter 2021 as vaccinations help us combat Covid."
Mr Dunne, MP for Ludlow, said that the end to uncertainty would be a major boost for business.
He said: "We have had four and a half years of uncertainty about the future trade relationship with Europe which now becomes clear, and we will retain many of the commercial benefits of trading with Europe, without the political challenges."
Wrekin MP Mr Pritchard said: "This is a huge and historic breakthrough. A tariff free £660bn trade deal with the EU is an amazing achievement for the PM and for the country.
"This deal also returns control of our laws, borders and immigration and standards while returning to a free, independent sovereign coastal state.
"January 1 will be the first day of a new global and free trade era for the UK."
Mr Kawczynski, who represents Shrewsbury & Atcham, said: "I would like to pay tribute to David Frost, the Prime Minister and the British team who have represented British interests in negotiations. Negotiating with the EU is an extraordinarily difficult and complex process and I am pleased a deal has been secured."
He added: "The compromise on fish is something I will be reading more acutely over the coming days but from what I have seen of the deal I am minded to support it when it comes for ratification to the House of Commons."
Montgomeryshire's Mr Williams, who was previously part of the Brexit negotiating team, said he welcomed the agreement, which would end uncertainty for farmers in his constituency.
He said: "Clearly the devil is in the detail but on the face of it tariff free, quota free access for our agricultural community, talking to farmers, they are over the moon, I am over the moon. This represents a future relationship that is good for Montgomeryshire.
He added: "Downing Street has been very clear that everything promised in that 2016 referendum has been made."
Mr Paterson said: "This has gone on since June 2016 and I very much hope it has delivered what everyone voted for but I will wait and see the analysis of the text before reaching a conclusion."