The U.S. will also be opening a new compound for its de facto embassy in Taiwan, a self-ruled island that China claims as its own and has been a longstanding flashpoint between Washington and Beijing.
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.
The completion of the new AIT offices - built over nine years at a cost of $250 million - comes amid closer US-Taiwan ties.
"The opening tomorrow of the new AIT headquarters shows how important our relationship is to the United States", the Republican lawmaker from MS said. Among officials attending Tuesday's ceremony was Taiwan's President Tsai Ing-wen, whose independence-leaning administration Beijing has sought to isolate diplomatically and threatens with invasion.
The site spreads over 6.5 hectares, including Chinese gardens, in Taipei's Neihu district.
Mr Trump in March signed the Taiwan Travel Act, which will allow more official visits between the USA and Taipei.
"The new office complex is a symbol of the strength and vibrancy of the US-Taiwan partnership in the 21st century".
Royce is a wife of Republican Ed Royce, chairman of the House of Representatives Committee on Foreign Affairs, a politician who has promoted several pro-Taiwan bills, including the Taiwan Travel Act, South China Morning Post (SCMP) reports. AIT's Taipei office has nearly 500 American and local employees, while its Kaohsiung branch has more than 30 staff.
The U.S. severed official diplomatic ties with Taiwan in 1979 to uphold Beijing's "One China" policy, which maintains that the breakaway territory is part of the People's Republic and can be reunified by force, if necessary.
Tsai hailed the complex as a new chapter in the "great story of US-Taiwan relations".
The Global Times, a widely-read Chinese state-run newspaper, said China should warn Taiwan and the United States against any provocation.
"The mainland must continue to build up its deterrence against Taiwanese authorities, making them know that the USA can not be their savior", it said in an editorial on the opening of the new office.