The news was broken just before 5am Pacific Time (1pm UK time) by Peter Currie, a Silicon Valley finance professional who is one of Twitter's board directors.
Currie's tweet included a link to a regulatory document filed with the US Securities and Exchange Commission, which said Dorsey had been appointed on 30 September.
Shortly after Currie's tweet, Twitter's own investor relations account tweeted the news.
Twitter's IR account also confirmed the promotion of Adam Bain to the role of chief operating officer; that former chief executive Dick Costolo had stood down from the board; and that Dorsey remained CEO of sister online payment business Square, but had stepped down as Twitter chair.
The SEC filing detailed that Dorsey, who is 38 and is one of Twitter's four co-founders, had served as interim CEO of Twitter since July, and before that as CEO between 2008 and 2009. He has been working at Square since February 2009 and serves on the board of directors of The Walt Disney Company.
Dorsey also shared the news in a series of tweets.
???? Hello! We have some news to share!— Jack (@jack) October 5, 2015
Dorsey was congratulated on his appointment by fellow members of the company's board including former Pearson CEO Marjorie Scardino and Peter Fenton, general manager of the venture capital firm Benchmark.
Inspired by the energy and clarity of purpose for Twitter that @jack brings as permanent CEO, even more so after a full search— Peter Fenton (@peterfenton) October 5, 2015