Batsman Joyce, 34, took over the captaincy at the end of July after Michael Yardy stood down from the role.
Sussex cricket manager Mark Robinson said: "Ed stepped in to Michael's shoes seamlessly last season and formed a strong alliance with Nashy.
"They both bring a wealth of experience and knowledge and I am excited at working with them."
Ireland international Joyce, who led the Hove outfit in four County Championship and five CB40 games last season, said it was "a great honour and privilege" to continue leading the side in 2013.
"I hugely enjoyed doing the job for the last few months of the season and I feel very strongly we can bring some silverware back to Hove next year," he said.
"With Murray Goodwin moving on and Rory Hamilton-Brown re-signing, the team will be slightly in transition next year.
"But it should also be a very exciting time for the club with a younger side and perhaps some more opportunities for the younger members of the squad to show what they can do.
"We will all be working as hard as possible to try and bring as much success as Yards has had in his time as captain."
Sussex have confirmed Ed Joyce will remain as captain next season, with Chris Nash appointed as vice-captain.