Speaking at the Conservative Party conference, she promised to introduce legislation next year for the "biggest overhaul" of the system in "decades".
And she said those against her plans were "defending the indefensible".
It comes after it emerged this week that the UK considered sending asylum seekers to an island in the Atlantic.
Ms Patel said changes "would take time" and she would "accelerate the UK's operational response" to the issue in the meantime.
The chief executive of charity Refugee Action, Stephen Hale, said it was a "positive step" for the home secretary to "realise what we've been trying to tell her - the asylum system is not fair or effective".
But he urged her to push for "quicker decisions and better support" for those seeking asylum in the UK.
Labour's shadow home secretary Nick Thomas-Symonds accused the Conservatives of being "the political party that broke" the asylum system, having been in power for 10 years.
He added: "Recent experience suggests they have not learned any lessons at all, with unconscionable, absurd proposals about floating walls and creating waves in the English Channel to push back boats and sending people thousands of miles away to process claims.
"The truth is the Tories are devoid of compassion and competence."
Ms Patel pledged to introduce a new asylum system that welcomed people through "safe and legal routes" and stopped those arriving illegally "making endless legal claims to remain".
The system will include expediting the removal of those "who have no claim for protection", she said.
She added: "After decades of inaction by successive governments, we will address the moral, legal, practical problems with this broken system. Because what exists now is neither firm nor fair.
"I will take every necessary step to fix this broken system amounting to the biggest overhaul of our asylum system in decades."
The promised overhaul follows record numbers of people making the journey across the English Channel to the UK in September, which Ms Patel has vowed to stop.
According to Refugee Action, 35,566 asylum applications were made in the UK in 2019 - down from a peak of 84,000 in 2002.
At the same time, delays in processing UK asylum applications have increased significantly.
Four out of five applicants in the last three months of 2019 waited six months or more for their cases to be processed.
Ms Patel said the UK would make more "immediate returns" of people who arrived illegally "and break our rules, every single week".
Refugee Action's Stephen Hale said to make the system fair her "immediate priority" should be to "honour her words and commit long-term to creating safe and legal routes for refugees to reach the UK" - including restarting settlement schemes that were paused during the coronavirus outbreak.
Pre-empting criticism of her proposals, Ms Patel said she expected some would "lecture us on their grand theories about human rights".
But, she added: "Those defending the broken system - the traffickers, the do-gooders, the lefty lawyers, the Labour Party - they are defending the indefensible".
It comes after it emerged this week that the government had considered building an asylum processing centre on a remote UK territory in the Atlantic Ocean.
Ms Patel asked officials to look at asylum policies which had been successful in other countries, the BBC was told.
Labour said the "ludicrous idea" was "inhumane, completely impractical and wildly expensive".
During her speech, the home secretary said the government would "explore all practical measures and options to deter illegal migration".
She added: "A reformed system will prosecute the criminals and protect the vulnerable. That is what a firm and fair system should look like."
Andy Hewett, head of advocacy at the Refugee Council, said he agreed with Ms Patel that the current system was "broken" and "leaves vulnerable people languishing for months on end, fearful for their future and unable to start rebuilding their lives".
But he said it was wrong to say it was illegal for people to arrive in the UK via small boats for the purpose of seeking asylum - which is covered in the UN Refugee Convention - although they would like to see fewer people attempting the dangerous journey.
"To this end, we're calling on the home secretary to restart the resettlement programme without delay, dismantle the inhumane family reunion rules that prevent parents from being reunited with their children in the UK, and introduce humanitarian visas so that refugees can travel safely to the UK," added Mr Hewett.