The Pilgrims are currently in the npower League Two relegation zone and have been without a boss since they sacked Carl Fletcher on New Year's Day.
Sheridan has previously been in charge at Oldham and Chesterfield but has been without a job since the latter relieved him of his duties back in August.
Argyle owner James Brent revealed Sheridan's track record in the lower leagues impressed him after he won the League Two title and the Johnstone's Paint Trophy with the Spireites.
Brent told the club's official website: "John has a proven record of leading clubs to success in Leagues One and Two.
"John impressed the interviewing panel with his commitment to excellence and his approach to moving the club up the league table.
"He expressed an enthusiasm for attacking football and was confident in his analysis of what we needed to do to succeed."
Sheridan himself highlighted the club's potential and insists he believes the club can avoid dropping out of the Football League.
He said: "I am very privileged to get this opportunity to manage the club. Everyone I've talked to says what a good club it is and what potential there is.
"I am very confident I can get us out of the position we are if everyone - the players and fans - work together."