Priti Patel said, for the first time, people seeking protection as refugees would have their claim assessed based on how they arrive in the UK.
She said ministers would crack down on people smugglers because "enough is enough".
Labour said the plans lacked compassion and competence.
Under the changes, people who arrive in the UK by what the government call illegal means to claim asylum will no longer have the same entitlements as those who arrive through proper channels.
There were 35,099 asylum claims made in the UK during the year ending March 2020, with Iran, Albania and Iraq providing the most applicants.
More than 8,000 people crossed the Channel in small boats, with the help of people smugglers.
Setting out the plans to MPs, Ms Patel said the government would introduce a "faster and fairer" system that would "better support the most vulnerable".
Ms Patel said "serious organised criminal gangs" were exploiting people trying to get to the UK, and that it was these same gangs who were also involved in "serious violent crimes" in the UK such as trafficking guns and drugs.
"Families and young children have lost their lives at sea, in lorries and in shipping containers having put their trust in the hands of criminals," she added.
"The way to stop these deaths is to stop the trade in people that causes them."
She said the new measures will create "safe and legal routes", and that people should be claiming asylum in the EU country in which they first arrive, rather than using it as a springboard to reach the UK.
"If you illegally enter the UK via a safe country in which you could have claimed asylum, you are not seeking refuge from imminent peril, as is the intended purpose of the asylum system, but are picking the UK as a preferred destination over others," she said.
She said the system was currently "clogged up" with bogus claims and legal wrangles.
But human rights lawyers have warned the plans are unlawful because they ignore Britain's international obligations under the Refugee Convention.
Labour said the proposals would do "next to nothing to stop people making dangerous crossings" or to deal with criminal gangs.
There are two enormous legal elephants trumpeting away in the shiny glass atrium of the Home Office that are casting some really significant doubts on whether the home secretary's plan is deliverable.
Firstly, can she treat some refugees who have a recognised case for protection differently from others, purely based on how they reached the UK?
Under the UN Refugee Convention (which, history fans, the UK government helped write in 1951) states can't penalise people in need who come "directly" from their homeland - or anyone who has "good cause" to enter a nation illegally.
Official sources say Ms Patel's restrictions would be legally possible because asylum seekers are not allowed to go "shopping" for the best destination.
But even if the restrictions are introduced, and the Home Office wants to send people back to France or elsewhere, how is that going to happen?
The UK has no legal agreement with EU nations to take these people back.
And that's because we chose to leave it as part of Brexit. The BBC has learnt that the Home Office has not sent any failed asylum seekers back to EU states since the end of the Brexit transition three months ago.
The home secretary's plans for asylum rely on striking agreements with other safe countries who would be willing to take people who have passed through their territory on the way to the UK.
Labour's shadow home secretary Nick Thomas-Symonds told MPs the changes proposed by the government "risk making the situation even worse for victims of human trafficking as it would make seeking help in the UK even harder".
"The government policy is defined by a lack of compassion and a lack of competence, the plans risk baking in to the UK system the callousness of this government's approach," he said.
Responding to Ms Patel's pledges, Refugee Council chief executive Enver Solomon accused the government of "seeking to unjustly differentiate between the deserving and undeserving refugee" by giving protection "based on how they travel to the UK".
Madeleine Sumption, director of the Migration Observatory at Oxford University, said it was "slightly misleading to say people have a choice between the legal and illegal route" adding "for many people the clandestine means will be their only way to get to the UK".
She also said there would be "complex issues" about whether other countries would be willing to take back asylum seekers deemed to have arrived in the UK via irregular routes.
Asked if any EU states had agreed to take people back, Ms Patel replied that she was currently in discussions with those countries.
There was support from Conservative MPs in the Commons, including West Bromwich MP Shaun Bailey who said: "Just like my constituents, I'm angry at the images that we're seeing of small boats coming into the Channel and the sky-rocketing costs of our asylum system.
"The broader issue here is this: our European neighbours need to step up. It's as simple as that."
What do the new proposals promise?
The Home Office said that "for the first time" the question of whether asylum seekers enter the UK via another "safe" country, such as France would "have an impact" on how it dealt with claims.
The government would seek the "rapid removal from the UK" of rejected applicants, with appeals "reformed to speed up" the process, it added.
But asylum seekers fleeing persecution or violence and coming to the UK via the "legal resettlement" route from countries such as Syria and Iran would straight away get permission to remain in the UK indefinitely, the Home Office said.
Under the new plans, anyone who pays criminal gangs to bring them to the UK would only ever receive temporary permission to remain and would be regularly assessed for removal from the UK.
Other proposals include bringing in "rigorous" age checks to stop adults entering the country by pretending to be children.
The use of hotels to accommodate arrivals will end and the government will bring forward plans to expand the "asylum estate".
Ms Patel said asylum applicants with criminal records who returned to the UK after being deported would receive a jail sentence of up to five years. The current maximum is six months.
And people smugglers - responsible for shipping many of the 8,500 people who crossed the English Channel in small boats last year - could get life sentences.