The Internet company said on Thursday that recently launched products and partnerships have set the stage for it to expand its audience.
The optimistic comments, as well as fourth-quarter revenue that topped analyst forecasts, were well received by investors. Twitter's stock jumped 9 percent to $45 in after hours trading.
"The stock is going to be up, because it's probably better than what people expected. But now they have to deliver," said Wedbush Securities analyst Shyam Patil.
"You can't jump on the bandwagon based on the commentary; you've got to see the numbers come through," he said.
Twitter has struggled to grow the number of users on its service, raising questions about whether it can achieve the scale of social network Facebook Inc, which has 1.39 billion users, or even fast-growing messaging and photo apps such as WhatsApp and Instagram.
CEO Costolo is facing mounting criticism on Wall Street, with many analysts and investors frustrated by the company's slow growth and seemingly constant shake-ups in its upper ranks.
In a conference call with analysts on Thursday, Costolo confirmed media reports that Twitter has struck a partnership with search engine Google Inc. The partnership could help bring its service to a broader segment of the public, Costolo said.
Costolo showed that he is really focused on improving the products and on the consumer experience, said JMP Securities analyst Ronald Josey.
Twitter reported a sharp slowdown in its user growth in the final three months of 2014, adding a scant 4 million monthly users to bring its total audience size to 288 million users.
Twitter blamed the weak user growth, which represented the slowest pace in at least three years, on a bug in Apple Inc's  recently launched iOS8 mobile software as well on "seasonality."
But Twitter executives said they expected user growth to pick up again in the first quarter, likely netting between 13 million and 16 million new users.
Twitter needs to shift investor attention to its financial performance and away from user growth, said Pivotal Research analyst Brian Wieser.
"Anyone who believes that users are everything are still going to be concerned, because they're still going to say that Instagram is bigger," he said.