The three women are scheduled to visit their children - who have been held since July when they were arrested along the Iraqi border - and seek meetings with top Iranian officials. Iran's state-run Press TV said the weeklong visas had been granted on an "Islamic humanitarian basis."
The mothers said they will appeal to Iranian leaders to release their children from prison.
Nora Shourd, Cindy Hickey and Laura Fattal wore long black headscarves as they left their flight from Dubai at Tehran's main international airport south of the capital. They passed through routine customs and passport checks as well being fingerprinted - a requirement imposed on Americans in retaliation for U.S. immigration controls on Iranians.
They were met by envoys from the Swiss Embassy, which represents U.S. interests in Iran, and taken in embassy vehicles from the airport. The Swiss ambassador to Tehran presented them with flowers at the airport.
"We are here to visit our children that we haven't seen for 10 months. We miss them very much," said Shourd in a trembling voice before bursting into tears.
"We hope to take them back," she said as tears rolled down her cheek.
Their arrival came a day after the United States said it had won support from other major powers for a new set of sanctions against Iran over its suspect nuclear program.
Iran has accused the three Americans - Sarah Shourd, 31; her boyfriend, Shane Bauer, 27; and their friend Josh Fattal, 27 - of spying. Their relatives reject the accusation and say the three were hiking in Iraq's scenic and largely peaceful northern Kurdish region.
Their lawyer, Masoud Shafii, told The Associated Press the mothers are seeking meetings with officials involved in the case, and ideally with top Iranian leaders, including President Mahmoud Ahmadinejad and supreme leader Ayatollah Ali Khamenei, who has the final say in all state matters.
Although the Americans have not been publicly charged, Shafii left open the possibility of a resolution outside of usual legal channels.
"Anything is possible," he said when asked whether the three might be released soon. "It doesn't have the feel of a normal court case."
Shafii plans to meet the mothers in Tehran and said they would visit the three detainees on Thursday. He said he has not yet been granted access to his clients.
Shafii said it was unclear whether they would meet at Tehran's notorious Evin prison where the three are being held or at another location.
"We have to wait and see ... but I think they are going to be given enough time with their children," he said.
The United States announced Tuesday that it has agreed with China, Russia and other major powers on a proposal for "strong" new sanctions against Iran, but they now face the challenge of getting backing from the rest of the U.N. Security Council.
The U.S., which has not had formal diplomatic relations with Iran since the 1979 Islamic Revolution, and its allies accuse Tehran of seeking nuclear weapons. Iran insists its nuclear program is for peaceful purposes.
Shafii said that "Inshallah," or "God willing," his clients would eventually be freed when asked about the new sanctions push. But he added that ongoing tensions between the U.S. and Iran "definitely ... has a direct effect on the case."
In recent years, a number of foreigners held by Iranian authorities on espionage and other security-related charges have been released following months of detention.
Last week, Iran freed French academic Clotilde Reiss, 24, after more than 10 months in jail. She was convicted of provoking unrest and spying during unrest that broke out after June's disputed presidential elections. Her supporters said she was targeted for an innocuous e-mail to friends describing the events unfolding around her.
A graduate student imprisoned for a month in Iran and barred from leaving the country for nearly a year returned home to Los Angeles in August. Esha Momeni, 29, was charged with acting against Iran's national security and held mainly in solitary confinement after conducting research on the Iranian women's rights movement.
An Iranian-American journalist, Roxana Saberi, who was arrested in January 2009, convicted of espionage and sentenced to eight years in prison, was released on an appeal in May 2009. An American academic, Haleh Esfandiari, was arrested in May 2007, accused of conspiring to overthrow the government, and freed three months later.
Nora Shourd said she worried especially about the effect that near-solitary confinement may be having on her always social daughter. With no one to talk to, Sarah had become seriously depressed, Nora Shourd says she was told by the Swiss diplomats who visited the trio last month. The diplomats also reported that Sarah was suffering a serious gynecological condition, while Bauer had a stomach ailment.
The mothers said their children have spoken to relatives only once by telephone, on March 9, for just a few minutes.
"We're going over as mothers to ask for humanitarian relief and we're very confident," Hickey said from a hotel in midtown Manhattan before leaving Tuesday. "We want to bring our kids home."
Hickey lives in Minnesota, Shourd is from Oakland, California, and Fattal is from suburban Philadelphia.