The US switched diplomatic recognition to Beijing in 1979 but maintains close economic, political and security ties with Taiwan.
"I offer you this", he said, "a tangible symbol that the United States is here to stay".
Taiwan President Tsai Ing-wen said the new complex reaffirmed the "vital relationship" between Washington and Taipei.
The new building is a significant upgrade from the low-key military building that AIT has used for decades and will serve as the representative office later this summer, said AIT Director Kin Moy at the opening ceremony.
"I look forward 2 an even brighter chapter in our enduring friendship!"
China claims self-ruled Taiwan under its "one China" policy and Beijing has never renounced the use of force to bring what it sees as a wayward province under its control.
Donald Trump's administration is moving to strengthen ties with Taiwan in the face of China's diplomatic moves and military threats.
"We urge the United States to honor its pledges made to China on the Taiwan issue, correct its wrong practices to avoid damaging China-U.S. relations as well as peace and stability across the Taiwan Strait", said Geng. Last month, Burkina Faso severed official ties with Taiwan in favor of China, leaving just 18 countries around the world that recognize the government in Taipei.
Royce is the highest ranking State Department official to visit Taiwan since 2015.
Beijing has broken off contact with Taipei since President Tsai, the leader of the independence-leading Democratic Progressive Party, was elected president in 2016 and refused to acknowledge that Taiwan is part of China.
The US, like many other countries, holds no formal diplomatic relations with Taiwan. "China's pressure on Taiwan is inciting a backlash from the public here".
Taiwan has lobbied Washington to sell it more advanced equipment, including new fighter jets, to bolster its defenses.
In the past few months, the Trump administration also angered Beijing by authorizing United States manufacturers to sell submarine technology to Taiwan, as well as enacting the Taiwan Travel Act to encourage official visits between the U.S. and the island. "There's no escaping the fact that this is a significant symbol of the enduring U.S. commitment to Taiwan".
Kharis Templeman, a social science research associate at Stanford University's Walter H. Shorenstein Asia Pacific research center, said that given the delicate nature of the summit in Singapore, the Trump administration may have chosen not to use the occasion to make a strong symbolic statement.
"Hence a few moves to loosen the previous self-limitations by Washington in its relationship with Taiwan", said Roy.
The site spreads over 6.5 hectares, including Chinese gardens, in Taipei's Neihu district.