Hendon takes over from Mark Robson, who stood down as Gills number two for personal reasons in May.
Andy Hessenthaler told BBC Radio Kent: "He was always my number one target, he's experienced at this level."
"He's been a player, an assistant and a manager in this division, I asked the question and he decided he wanted to do it.
I've spent the last two weeks putting a new structure in place, which included Ian Hendon.
Dover Athletic chairman Jim Parmenter
It means Dover are starting the search for a new manager for the second time since the season ended.
Their chairman Jim Parmenter told the Dover Athletic official website: "I'm upset because we released Andy from his contract here to enable him to take the Gillingham job.
"But since then he has taken Darren Hare from our youth academy, which was a huge blow for us and I've spent the last two weeks putting a new structure in place, which included Ian Hendon.
"And now he has actually taken our manager, the person he gave a reference to for the job in the first place.
"As far as I'm concerned, a line has been crossed."
Source: BBC Sport
Source: BBC Sport