The defender has agreed to join the Louth outfit for the 2014 Airtricity League campaign after a brief spell with Shelbourne last season
Andrews, who played with Shelbourne last season, becomes Horgan's 14th signing and joins the Drogs for a second spell after previously lining out for the club's youth teams.
"I am delighted to be re-joining Drogheda United after a five year spell over in America," Andrews told the club's official website. "I know what a great club it is first hand and after speaking with Robbie and hearing his plans I am very excited for the season ahead."
The 23-year-old's early career saw him play for Shelbourne and Drogheda United before earning a sports scholarship with Northern Kentucky University. He later played for Mason Patriots at George Mason University before returning to Ireland.
Drogheda boss Robbie Horgan revealed that Andrews had been in talks with clubs in England before agreeing to re-join the club.
"Paul is a very promising player and I believe that he will develop even further with us," said Horgan. "He is a strong player and his height is a great advantage as a defender.
"I had heard that he was speaking to some English clubs and I felt that he could progress with us for another year or so before making the move across the water.
"I think he will complement the other lads very well and I'm very happy now with how the back line has shaped up."