In his article, Mr Gyimah said that if MPs were to support the agreement it would "set ourselves up for failure" by surrendering "our voice, our vote and our veto".
He also warned that the vote could be a "humiliating defeat" for the ruling Tory Party, especially with numerous backbenchers publicly expressing their opposition and threatening to vote against it in parliament.
Conservative MP Jacob Rees-Mogg, a staunch Brexiter who is one of the most vocal critics of the deal, said Friday that the government was trying to frighten people into accepting it with dire forecasts about the impact of leaving the European Union without an agreement.
However, fellow Brexiteer Jacob Rees-Mogg has written in the Daily Telegraph of an effort to "frighten and to gull (people) into acquiescing to a non-Brexit Brexit".
"These four parties don't seem to get it", Scottish Conservative interim leader Jackson Carlaw said.
Liam Fox will take a swipe at Tory opponents of Theresa May's Brexit deal on Friday, accusing them of not facing up to the fact she has had to make tough choices.
But hinting at potential further resignations from Mrs May's top team over Brexit, he added: "Members of the Cabinet who don't vote for the deal won't be members of the Cabinet".
Scottish political parties are uniting against the Brexit deal in a rare cooperation to show their disapproval with the UK's decision to leave the European Union.
The deal has been criticised by both eurosceptics and europhiles among her own Conservative Party lawmakers.
"I've got a plan". "In the lead up to what is a crucial vote, you will see more of that".
She added: "I think what we have seen revealed in numerous Labour Party's comments is that what they actually want is a general election, and that means they are not acting in the national interest, they are putting their narrow party interests first". "It's a People's Vote, with the option of keeping the best deal we now have as a member of the European Union".
"I think every MP needs to consider the importance of delivering on the Brexit vote together with the importance of doing that in a way that is good for their constituents, that protects their constituents' jobs and their livelihoods for the future".
The Observer can reveal that Starmer told a meeting of the shadow cabinet last Wednesday that Labour should be ready to "move quickly through the gears" to call a no-confidence vote in the government immediately if, as expected, May's blueprint is defeated when MPs vote on it on 11 December.
Downing Street are said to prefer a proposal put forward by the BBC for a December 9 tete-a-tete between the PM and Jeremy Corbyn, with Labour favouring a rival one-on-one offer from ITV.
Brexiteers have accused the government of betraying the 2016 referendum, as the deal could see the United Kingdom locked in the EU customs union long after the article 50 deadline.
She said: "If the vote is not supported, then we will see more division and more uncertainty for people".
He said he wanted to "pay tribute" to May's leadership in securing the deal.
May's comments came after lawmakers proposed an amendment that could stop Brexit if Parliament rejected her agreement.
Wales and Scotland say they have been ignored in the negotiating process, something the government denies.