Former U's defender Dunne, 39, who worked as assistant to Ward, has spent the last 16 years at the club.
He had been installed as caretaker manager earlier this week after Ward was relieved of his duties after losing 1-0 to Scunthorpe in a key relegation clash on Saturday.
Colchester's executive chairman Robbie Cowling said: "It was not an easy decision to part company with John Ward because he had worked so hard to achieve so much for Colchester United Football Club. However, it was an easy choice when it came to selecting John's successor.
"Joe has been with Colchester United for 16 years as a player, youth-team manager, reserve manager, assistant manager, caretaker manager and now he is first-team manager.
"Joe takes charge of Colchester United when the club's long-term prospects are the best they have ever been, but at a time when the short-term future is one of its most challenging.
"The investments we have made in our facilities and in the youth set up will pay dividends in the not-too-distant future and the land that the club owns in Tiptree could, if planning permission is granted, provide funds to put the club on a stable financial footing and allow it to continue those types of investments into the foreseeable future."