It’s official: Twitter has named Jack Dorsey permanent chief executive officer, to lead the social-media company he co-founded.

Even as he takes over the reins at Twitter, Dorsey, 38, will continue to serve as CEO of Square, the payments and financial-services company he co-founded in 2006. He also will continue to serve on Twitter’s board, but will no longer be chairman.

“My ability to run both Twitter and Square is made possible by the great teams at both companies,” Dorsey said during an investor call Monday.

Dorsey will rely on key lieutenant Adam Bain, who has been elevated to the position of chief operating officer. He previously served as Twitter’s president of global revenue and partnerships, and was short-listed as a potential CEO candidate.

Update: Twitter shares opened Monday at $26.99 per share (up 2.6%) on the news, announced prior to market open. After declining slightly in mid-morning, the stock rose throughout the day to close at $28.15, jumping 7% for the day.

With significant challenges facing Twitter, “we worry that a non-full time CEO (with the split role at Square) creates a more challenging environment than necessary,” RBC Capital Markets analyst Mark Mahaney wrote in a note.” Furthermore, he added, Twitter appears to be facing some real-employee retention issues… and the roll-out of Project Lighting” — a curated news service to let users follow events in real-time — “and the integrated marketing campaign have yet to happen (and will take time to prove).”

In June, Twitter’s board issued a statement that it would consider only CEO candidates “who are in a position to make a full-time commitment to Twitter.” That appeared to rule out Dorsey, with his Square obligations, but clearly any of the board’s concerns on this front were allayed.

Dorsey had served as Twitter’s interim CEO since Dick Costolo departed at the end of June after six years at the company. Twitter said Costolo resigned from its board effective Sept. 30; the company has commenced a search for a new outside director to serve as chairman.

Dorsey issued a series of high-level comments on his outlook for Twitter via @jack:

“Jack not only understands Twitter’s culture, but is a vital part of it,” board member Peter Currie, president of Currie Capital, said on the call. Twitter disclosed the management and board changes in a Securities and Exchange Commission filing.

Twitter said “there are currently no plans to provide Mr. Dorsey with direct compensation for his role as Chief Executive Officer.”

In the 13 weeks he served as interim CEO, Dorsey had already made several strategic decisions on the company’s direction. That included making management changes to the company’s product team and a new initiative exploring how to extend Twitter’s messaging beyond 140 characters.

In a tweet, Currie said the vote to bring on Dorsey as full-time CEO was unanimous:

Besides leading Twitter and Square, Dorsey also serves on the board of The Walt Disney Co.

The St. Louis native was Twitter’s original CEO when the company formed in 2006, but Dorsey clashed with his co-founders and stepped out of the role two years later to become chairman. On March 21, 2006, he posted the service’s first-ever tweet.