Ms Soubry, who has represented Broxtowe as a Tory candidate since 2010, is set to join the breakaway Independent Group of eight MPs who left the Labour Party earlier this week.
There will now be 11 Independent Group councillors.
The MP will join Conservative colleagues Sarah Wollaston and Heidi Allen as well as MP for Nottingham East Chris Leslie - who left the Labour Party alongside seven colleagues amid differences with Jeremy Corbyn on Brexit and anti-Semitism.
In a letter to the Prime Minister Theresa May, Ms Soubry and her colleagues suggest the party is “firmly in the grip of the ERG and DUP”.
Writing to her constituents about why she left the Conservatives to become an Independent Group MP, she said: “As you may have heard I have resigned from the Conservative Party and will now sit as an Independent.
“My decision to leave the Conservative Party, which I first joined over 40 years ago, has not been easy but I believe it is the right decision.
“I have explained my reasons in a letter sent this morning to the Prime Minister from myself and two other Conservative colleagues.
“On Monday a group of MPs resigned from the Labour Party and they are now sitting as members of the Independent Group and I will be sitting with them in Parliament.
“My decision will come as not much of a surprise to regular readers of this email newsletter.
“I have written of my belief that the Conservative Party is drifting to the right wing of British politics.
“I have also recognised that many constituents feel their views are not represented by either of the two main parties.
“Nottingham East MP Chris Leslie said on Monday in his resignation speech, “enough is enough”.
“I agree with him; in the last few years I have come to the firm view that I have more in common with his values and principles than many people in the Conservative Party. “It is time to realign British politics and get back to the centre moderate ground.
“If you can, I hope you might send me your support. In any event, I will continue with my work for all my constituents - in that respect nothing has, or will, change.”