The China Southern Airlines flight, from the southern city of Guangzhou, was the first of 36 cross-strait flights to be launched this weekend.
It carried about 250 passengers and was met with a water sprinkling ceremony.
Company chairman Liu Shaoyong flew on the inaugural flight.
"This is a sacred moment. The two sides of the strait are like members in one family," he told journalists in Taipei.
Other arriving passengers, many of whom are tourists, were greeted by lion dancers and aboriginal singers.
"It's so convenient to get here," Wang Qi, who arrived in Taipei from Xiamen, said.
"Since I was very young I always wanted to go to Alishan," she told Reuters news agency, referring to Taiwan's most famous mountain.
At the same time as the China Southern flight was travelling to Taipei, a Taiwan-based China Airlines flight with Taiwanese tourists was making its way to Shanghai.
The new flight agreement is being seen as a high-profile endorsement for new Taiwanese President Ma Ying-jeou, and his Kuomintang (KMT) party, which has just taken power again after more than a decade in opposition.
Departure and arrival footage of passengers
It strengthens the KMT's election stance that they are the party which can do business with the mainland.
Until now, people had to fly via Hong Kong or Macau to get to Taiwan
China and Taiwan ruled by separate governments since end of Chinese civil war in 1949
China considers the island part of its territory
China has offered a "one country, two systems" solution, like Hong Kong
As well as the symbolism, there's a practical hope too that the increase in mainland tourists will boost Taiwan's flagging economy.
Local businesses are predicting the new arrivals will provide a much-needed cash boost.
Tourist numbers from the mainland are expected to rapidly increase because - alongside the deal on flights - the two sides have also agreed that the number of Chinese tourists allowed to visit Taiwan will rise to 3,000 per day from 18 July.
Many Taiwanese are excited by the expected influx of tourists, says the BBC's Caroline Gluck in Taipei.
But others are more wary - citing concerns about rude behaviour, cheap spending habits and the potential for political disputes, our correspondent says.
Long road ahead
There is still much that could be done to improve China-Taiwan relations.
Direct cargo flights - much more useful to Taiwanese businesses than tourist flights - are still being blocked by Beijing.
And there is no sign of progress on political issues which are key for Taiwan, including Taipei's demand for international recognition.
The new charter flights still take a circuitous route, through Hong Kong airspace, so that flying times are longer than need be.
This is because Taiwan's military is on constant alert for an air attack from the mainland, and analysts say it cannot afford to let civilian flights clutter cross-straits radars.
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