Now that Jack Dorsey has been officially named the permanent CEO of Twitter, it's time for a shake-up at the company's board of directors, early Twitter investor Chris Sacca said Tuesday.

"I think this board was inactive for too many years, saw the writing on the wall for some of these problems that we're hitting in terms of growth and didn't act when they should have acted before," the founder of Lowercase Capital said in an interview with CNBC's "Closing Bell."