The Spitfires manager replaces Chris Kinnear who left the Whites after five years on Friday.
Hessenthaler took Dover to back-to-back promotions from the Ryman South to the Conference South during his spell as player-manager.
The former Gillingham midfielder had just taken Eastleigh to four straight National League wins.
Their push for the play-offs is a far cry from what he now faces in his new role
Dover are in big trouble down the bottom and on Saturday lost 4-1 to Salford. They haven’t won since August.
Their chairman Jim Parmenter said: “We are delighted to be able to move so quickly to secure Andy’s services and we are now looking forward to working with him and his team.
“This is a brand new chapter for the football club and it starts right now.”
Eastleigh chief exec Kenny Amor said: “We are hugely disappointed to lose Andy. Following conversations, it seems geography has won in this case.
“This was not something that the club had anticipated, however we will move swiftly to appoint the right candidate to continue the good work which has already been started this season.
“The club still remains very ambitious to succeed this season and despite this setback we will make sure whoever takes this role is equally as ambitious.”