Mr Capellas will take over from interim WorldCom chief executive John Sidgmore.
"I took this job because I am convinced that WorldCom has the assets, the customers and the people to regain a leadership role in this industry," he said in statement.
"In order to do this, we must first regain trust and win respect."
WorldCom filed for the largest bankruptcy in US history in July after an accounting scandal which saw the company restate its profits by more than $9bn.
Mr Capellas said the company was more stable now, with cash reserves of $1.4bn and a restructured the broad, accounting department and audit team.
Future calls
"I have spoken to many groups - creditors, managers, and board members - and it is everyone's desire to see this company succeed," Mr Capellas said.
There was no indication from the company what role the current chairman, Bert Roberts, and chief executive, John Sidgmore, would retain.
Mr Sidgmore took over as chief executive in April when Bernie Ebbers resigned.
The second largest long-distance US phone carrier, which also transmits almost half of the world's internet traffic, is saddled with $40bn in liabilities.
WorldCom still faces criminal and regulatory investigations in the US over accounting fraud.
Mr Capellas was the chief executive of computer maker Compaq before it merged with rival Hewlett-Packard last year, after which he became president of the combined group.