The Northampton Town boss appeared to be heading for The Valley.
Wilder led the Cobblers to the League Two title this season and is in high demand as a result.
Bolton Wanderers were credited with an interest by HITC sources last month, but Charlton appeared to have won the race having been granted permission to talk to the 48-year-old this week.
However, Wilder's proposed move to The Valley is now off, as confirmed by a statement on the Addicks' website on Wednesday.
It read: "Charlton Athletic can confirm that following discussions with Northampton Town manager Chris Wilder and his assistant Alan Knill over the vacant managerial role at The Valley, the club has been unable to reach an agreement.
"The club will now continue its search for a candidate to take the club forward."
The South London press are now claiming that Sheffield United, who will face relegated Charlton in League One next season, are "primed to come in for" the Cobblers manager.
Wilder hails from Stocksbridge, a small town on the outskirts of Sheffield, and is a known supporter of the Blades, who finished a disappointing 11th this season.
As a result, the Sheffield Star reported on Tuesday that Nigel Adkins' position as manager at Bramall Lane is hanging in the balance.
United, who were relegated to the third tier in 2011, are on to their fourth permanent manager in that time.