Jack Dorsey will be named permanent Twitter CEO as early as this week. Dorsey will run both Twitter and Square, which is expected to file for its initial public offering in the coming weeks. Thomas Samson/AFP/Getty Images

It took nearly 140 days, but Twitter has finally decided to name co-founder Jack Dorsey as its permanent CEO, according to a report. The decision, which is expected to be made official as early as Thursday, has already driven company stock up nearly 3 percent.

Dorsey, who co-founded Twitter in 2006 and previously served as its CEO, has been running the social network as interim chief since June, when previous leader Dick Costolo stepped down. Since then, Dorsey has been busy making widely welcomed decisions, such as removing the 140-character limit previously placed on private messages between users. The decision to hire Dorsey permenantly was first reported by Re/code, which cited unnamed sources.

Under Dorsey's leadership, Twitter has been ramping up its release of products, launching something new nearly every couple of weeks and testing and innovating with what the company has to offer. This focus on products made Dorsey a popular choice with those inside the company as well as Wall Street.

“The more the product simplifies, the more the product seems straightforward," Dorsey told CNBC in June. "The more we ship and execute, the more we will have going forward."

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The Twitter board in mid-June tried to pressure Dorsey into leaving Square by announcing that its CEO post was a full-time job, implying the board would not allow Dorsey to head both Square and Twitter, but ultimately Dorsey proved his worth during his four months as interim chief.

"The outside world really can't see this yet, but we've made massive changes in the time in terms of the product ... Jack is partly responsible for that. He also has been great in terms of challenging the teams on things that maybe we hold sacred and dear," Adam Bain, Twitter's head of revenue, told the Telegraph. Bain had been considered a top candidate for the CEO job but refused to take it if Dorsey was interested in the position, according to Re/code.

Besides heading Twitter, Dorsey is also expected to remain the CEO of Square, his mobile-payments tech company that is expected to file for its initial public offering in the next few weeks. As CEO of two tech giants, Dorsey will join the ranks of Elon Musk (CEO of Tesla Motors and SpaceX), Steve Jobs (Apple and Pixar) and Jeff Bezos (Amazon and Blue Origin).

"This is not a surprise," said Johnny Won, founder of Hyperstop, a tech consultancy firm. "Jack Dorsey has always been the strongest candidate and now he’s CEO on his own terms since Twitter’s inept board tried of force him to pick Twitter over Square and couldn’t make him do it. The board is responsible for crashing Twitter’s stock to its all-time low in August and Jack Dorsey now has one of the hardest jobs in Silicon Valley."

As Dorsey steps into the job his biggest challenge will be helping Twitter gain new users so that the company continues to grow its advertising revenue. The social network has seen its growth in monthly active users slow down drastically over the past two years due to lack of innovation and as a result of the complicated way the Twitter works, but already, Dorsey has introduced many ideas that could make the product more accessible to new users. For example, Dorsey is also considering getting rid of the 140-character tweet limit and letting users share longer posts.

"He doesn't seem to suffer from the denial that characterized much of Dick Costolo's tenure, but instead seems to understand the scale of the challenge Twitter faces," Jan Dawson, chief analyst at Jackdaw Research, said. "Most importantly, he appears to want to drive growth by making the core Twitter product better rather than trying to redefine the Twitter audience. Under his interim leadership, Twitter has already taken some big steps forward, but I suspect there's a lot more to come if he stays on."

Short term, Dorsey will also have to lead Square as it goes through the challenging process of becoming a publicly traded company and convince potential shareholders that his split focus on Twitter won't detract from his abilities of running Square.

"Square’s IPO will be a challenge but Jack Dorsey currently has the unique credentials to credibly provide product vision to Twitter," Won said.