Sheridan joined the Pilgrims as caretaker boss in January following the departure of Carl Fletcher and helped the club to avoid relegation from League Two.
The former Oldham Athletic and Chesterfield manager has put pen to paper on a deal which will keep him at Home Park until 2016.
"I am very, very pleased and very happy to get it all sorted out," Sheridan told the club's official website. "Obviously, now the hard work starts. I keep saying it - I'm ready to get this club pushed up the league, and that's what I am going to try to do.
"It's not going to happen overnight. The club, for the last two, three, four years, have been struggling at the wrong end of the table, and it's important that I try to get the club back to where it was only four or five years ago.
"With three years, I can settle, and everyone will get used to how I'm working, and I am positive I will get them where we want to go."
Sheridan won promotion from League Two as Chesterfield boss in 2011.