Musk said he wanted to help purge bots on Twitter before citing it as a reason not to complete the deal.
The move completes Dorsey's exit from which began last year when he resigned as CEO.
The CEO blamed the economy for what is set to be the tech company's worst day ever.
After weeks of will-he-won't-he, the world's richest man has purchased the social media company for approximately $44 billion.
