"The reason why Evan and I hired Dick in the first place is because we admired his leadership skills," Stone said Friday on CNBC's "Squawk Alley." "We've known him to be a great leader, a really funny guy, and that was always a key hiring personality at Twitter: Are they funny?"
In fact, Stone added, "Dick is a hilarious guy, which is important because humor is kind of a secret delivery mechanism of truth."
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Stone's comments come at a time when some investors and industry watchers have questioned whether Costolo is the right leader for Twitter. In December, Harvard Business School professor Bill George told CNBC that Costolo lacked product leadership, was inflexible, and was not in the same league as tech chiefs like Google's Larry Page or Facebook's Mark Zuckerberg.
The executive bench at Twitter is very deep and talented, Stone said. He singled out Adam Bain, Twitter's president of global revenue, as someone who is incredibly good at his job.
He also said Twitter has a lot of room to grow and remains an important tool for the world.
"Everything that's happening in the world is coursing through Twitter, and there are so many more things that need to course through Twitter, and all of that of course can be monetized through their native platform," he said.
Twitter is an example of a company with inherent value because it delivers instant news around the world, he said. "History has shown that when you get information quicker than the other guy, you do better."
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LinkedIn is another example, he said, because it provides a tool that job recruiters use every day and helps people find employment.
He said lofty valuations for tech companies can be appropriate, but warned some valuations are inflating simply because there is so much money in the venture capital world right now.
"When you go to raise money, you say, 'Well we need $3 million,' and they say, 'Don't you mean $30 [million]?'" he said.
Stone joined "Squawk Box" from the South By Southwest festival in Austin, Texas, where his company Jelly Industries is promoting its "Super" app. Launched last year, Super allows users to superimpose thoughts and opinions over images, which can be shared on social media sites like Facebook and Instagram.
Jelly recently announced a new function in Super called Explore that helps users find trending posts.
"The community right now is very strong, but they have little visibility into what others are doing," Stone said. "[Explore] really gives you a window into the very positive and energetic community that is going on in Super right now."
The expansion is part of setting the right tone for early adopters, he said. If social apps do not "kindle the right sort of positivity in a community," they "may go south very fast," he added.