Mr Johnson, who resigned his position in the Whips' Office a short while ago, said the decision was hardest he had "ever made".
The MP for Dartford - who backed Leave in the referendum - said he had been "hopeful that changes could be made to improve the deal with the European Union but it is now clear to me that no significant changes will be made".
"The 'back stop', contained in the agreement, gives our country no clear, unilateral path out of the European Union and ensures we will be fettered in our ability to negotiate trade deals with other nations in the future," he added.
"Along with near, two thirds of my constituents and a majority of the country, I supported 'leave' in the referendum as I wanted the UK to take back the sovereignty we had lost during our membership of the European Union.
"Unfortunately, this agreement prevents us taking back control and instead could leave us perpetual, constrained by the European Union."