The changes, which will be in place for a year before review, create new stages in the lawmaking process where the Speaker declares a Bill, or clause within a Bill, is English or English and Welsh only.
All MPs will continue to speak and vote on the existing legislative stages but only relevant MPs will be allowed to vote at the new phases.
The goal is to eliminate the anomaly where Scottish MPs in Westminster can vote on matters such as health or education in England, but English MPs cannot do likewise on issues devolved to the Scottish Parliament - the so-called West Lothian question.
The new rules, were approved after a bad tempered debate which heard complaints thait they would mean Scottish and Northern Irish MPs had second-class status.
Shadow Leader of the Commons Chris Bryant said the proposals were so complicated that they resembled a “bowl of soggy, overcooked spaghetti” and claimed they would hasten the break up of the United Kingdom.
The Labour frontbencher said: “I think Conservative and Unionist MPs in the end will rue the day if they vote for these measures because this is a charter for breaking up the union, not for keeping it together.”
Mr Bryant said the addition of up to six new processes to already complicated Commons procedure would not be understood by most MPs and the wider public.
“In years to come people will be running competitions to see if anyone can possibly explain these measures in fewer than 1,000 words and I bet you nobody will ever win that prize.
“Some have described all of this as constitutional knitting but knitting at least has a rhyme and a reason to it.
“This frankly will be a bowl of soggy, overcooked spaghetti,” he said.
DUP leader Nigel Dodds said: “Our profound fear is not what this does to or for England, which is very little in truth, but what it potentially does to the fabric of our union. Quite frankly, our union does not need any more rending.”
But Leader of the Commons Chris Grayling rejected suggestions the changes would exclude some MPs.
“The truth is actually it is nonsense. Despite all the rhetoric our proposals do none of that. What they do is bring fairness to our devolution settlement and it is fairness that will secure the future of our union,” he said.
Keighley MP Kris Hopkins claimed the issue was raised “time and time again” by constituents during the General Election campaign.
He said: “Many key financial and policy decisions, previously made in Westminster, have since been devolved to the Scottish Parliament, the National Assembly for Wales and the Northern Ireland Assembly, and I support this.
“But it no longer acceptable for MPs from those parts of the United Kingdom to be allowed to affect the exact same choices for people living in England.
“I am a strong supporter of the Union and believe the new arrangements will work to strengthen the bonds between our four nations, whilst giving English voters more of a say over our own destiny.”
The changes to the Commons procedures will be reviewed again after they have been in place for a year.