The goalkeeper moves to The Valley after leaving West Ham United and becomes new manager Bob Peeters’ eighth signing of the summer.
The 26-year-old, who has also represented Ipswich Town, Portsmouth, Bristol City and Bournemouth, told the club's website: “I'm very excited and can’t wait to get started.
"I’m delighted to get it done. It was a pretty sharp move and I’m very happy to be here."
Henderson worked with Charlton goalkeeping coach Ben Roberts at Yeovil Town three years ago.
He joins Yoni Buyens, Igor Vetokele, Andre Bikey, Franck Moussa, Tal Ben Haim, Johann Berg Gudmundsson and George Tucudean in the re-shaped Charlton squad for the new season.