In a statement posted to social media, Jenrick said: "It is with great sadness that I have written to the Prime Minister to tender my resignation as Minister for Immigration.
"I cannot continue in my position when I have such strong disagreements with the direction of the Government’s policy on immigration."
A source close to the former Home Secretary warned that the legislation will allow "every single illegal migrant to make individual human rights claims", saying it is a "further betrayal of Tory voters".
He added: "It is with great sadness that I write to tender my resignation as Minister for Immigration. I cannot continue in my position when I have such strong disagreements with the direction of the Government's policy on immigration.
"As you know, I have been pushing for the strongest possible piece of emergency legislation to ensure that under the Rwanda policy we remove as many small boat arrivals, as swiftly as possible, to generate the greatest deterrent effect.
"This stems from my firmly held position that the small boats crisis is a national emergency that is doing untold damage to our country, and the only way we will be able to stop the boats completely is by urgently introducing a major new deterrent.
"I have therefore consistently advocated for a clear piece of legislation that severely limits the opportunities for domestic and foreign courts to block or undermine the effectiveness of the policy.
"One of the great advantages of our unwritten constitution is the unfettered power of our sovereign parliament to create law, and that is a power we must take full advantage of. The Government has a responsibility to place our vital national interests above highly contested interpretations of international law.
"In our discussions on the proposed emergency legislation you have moved towards my position, for which I am grateful. Nevertheless, I am unable to take the currently proposed legislation through the Commons as I do not believe it provides us with the best possible chance of success. A Bill of the kind you are proposing is a triumph of hope over experience.
"The stakes for the country are too high for us not to pursue the stronger protections required to end the merry-go-round of legal challenges which risk paralysing the scheme and negating its intended deterrent."
"Reflecting on my time in the Home Office, I am proud of the improvements we have delivered together working alongside dedicated and capable civil servants. I am grateful to you for agreeing to much of my five-point plan to reduce net migration which, once implemented, will deliver the single largest reduction in legal migration ever.
"However, I refuse to be yet another politician who makes promises on immigration to the British public but does not keep them.
"This package must be implemented immediately via an emergency rules change and accompanied by significant additional reforms at the start of next year to ensure we meet the 2019 manifesto commitment that every single Conservative MP was elected upon.
"The consequences for housing, public services, economic productivity, welfare reform, community cohesion and, more fundamentally, for trust in democratic politics are all too serious for this totemic issue to be anything other than a primary focus for the Government."
While the Government's new legislation says UK parliament "is sovereign", noting that "the validity of an Act is unaffected by international law", Suella Braverman this evening warned that it is "fatally flawed".
James Cleverly signs new Rwanda treaty with Foreign Minister Vincent BirutaREUTERS
"It is a further betrayal of Tory voters and the decent patriotic majority who want to see this insanity brought to an end."
The new legislation also disapplies parts of the Human Rights Act, preventing it from getting in the way of sending migrants to Rwanda.
In a statement at the start of the legislation, Home Secretary James Cleverly said the Bill is not compatible with the ECHR.
Suella Braverman has hit out at Rishi Sunak's emergency legislation, dubbing it "fatally flawed"PA
He said: "I am unable to make a statement that, in my view, the provisions of the Safety of Rwanda (Asylum and Immigration) Bill are compatible with the Convention rights, but the Government nevertheless wishes the House to proceed with the Bill."
The law also states that Rwanda is "safe country".
In a statement posted to social media after the legislation was published, Cleverly said: "When we said we would stop the boats, we meant it.
"This Bill makes sure that parliament decides who comes to this country - not the criminal gangs or foreign courts.
"Action, not empty rhetoric, will stop the boats."