In the fourth quarter of last year, Twitter generated more than $1 billion in revenue, a first for the company. Advertising sales of $885 million during the quarter were up 12 percent from the same time in 2018. And the number of users who see ads on its platform on a daily basis grew 26 million in 2019, up 21 percent from the prior year.

But investors have complained that Twitter has failed to come up with innovative new products. Though its core social network remains prominent — it is one of President Trump’s primary bullhorns — upstart rivals including, most recently, TikTok, have seized the public’s imagination and eyeballs.

In October, Twitter’s shares fell more than 20 percent when it reported that it has missed Wall Street’s revenue expectations. (The company expects to stage a recovery this year, with major events like the Olympics and the U.S. presidential election drawing users and advertisers to its service.)

More of Mr. Dorsey’s wealth is concentrated in the financial company Square. He owns about 13 percent of the company’s outstanding shares, a holding worth about $4.9 billion as of Friday, while he controls about 2 percent of Twitter’s outstanding shares, worth about $531 million.

Mr. Dorsey was also not a regular presence at Twitter’s San Francisco office for much of last year, making it a point to travel the world, including to visit more than 30 of Twitter’s global offices.