The Daggers’ four-goal forward has agreed to play at the Gallagher Stadium.
New Stones boss Harry Wheeler has been looking to add to his firepower since arriving at the Kent club.
"He is a player that I have admired for a long time, and is someone who fits the same mould as the other players that have joined the club in recent weeks and those remaining who were here when we took over,” the manager said on the club's website.
“Elliott will add another goal threat to the side and leads by example with his work rate and character; he is a big part of our rebuilding process.”
The Stones have taken a player from a rival down the bottom of the table.
The Daggers are 22nd while Maidstone sit just a place outside the National League bottom four.