Sheridan joined the Pilgrims as caretaker boss in January after Carl Fletcher was fired, and he helped guide the club away from the League Two relegation zone.
Although they only confirmed their league status on the last day of the season, Sheridan did enough to earn a deal that will keep him at Home Park until the summer of 2016.
"I am very, very pleased and very happy to get it all sorted out," former Chesterfield boss 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."
Argyle's owner and chairman James Brent said: "I am thrilled that John has pledged his future to taking our club forward.
"The length of the contract emphasises that both he and the club see the relationship as a long-term one, focusing on taking us back up through the divisions.
"The deal gives both parties important continuity, stability, and the opportunity to make very real progress."