It comes following a scarcity of the necessary drugs in the wake of a European-led boycott of the substances for executions.
Republican governor Bill Haslam signed the bill into law on Thursday after lawmakers passed the legislation in April, the Associated Press reports.
Bill sponsor Senator Ken Yager explained he introduced the legislation “because of a real concern that we could find ourselves in a position that if the chemicals were unavailable to us that we would not be able to carry out the sentence.”
“This is unusual and might be both cruel and unusual punishment,” Richard Dieter, president of the Death Penalty Information Centre said in comments reported by CNN.
“No state says what Tennessee says. This is forcing the inmate to use electrocution,” he added, describing the electrical chair as a “brutal alternative”.
The drug shortage comes after European manufacturers banned US prisons from using their drugs in executions following a successful campaign by death penalty activists.
A Vanderbilt University poll released on Wednesday found 56 per cent of Tennesseans supported the law to allow electrocutions if lethal injection drugs were not available.
The state has not executed a death row inmate since 2009, in part because of difficulty in obtaining lethal injection drugs, The Tennessean writes.
It adds Tennessee has scheduled executions by lethal injection for at least 10 death row inmates.
Karla Faye Tucker: Executed Feb. 3, 1998; Age 38
Elliot Johnson: Executed June 24, 1987; Age 38
Ignacio Cuevas: Executed May 23, 1991; Age 59
David Goff: Executed April 25, 2001; Age 31
Robert Black Jr: Executed May 22, 1992; Age 45
Samuel Hawkins: Executed Feb. 21, 1995; Age 52
Leonel Herrera: Executed May 12,1993; Age 45
Miguel Richardson: Executed June 26, 2001; Age 46
Richard Beavers: Executed April 4, 1994; Age 39
Edward Green: Executed Oct. 5, 2004; Age 30
Tommie Hughes: Executed March 15, 2006; Age 31
Javier Cruz: Executed Oct. 1, 1998; Age 41
Willie Shannon: Executed Nov. 8, 2006; Age 30
Robert Thompson: Executed Nov. 19, 2009; Age 34
Randall Hafdahl Sr: Executed Jan. 31, 2002; Age 48
Franklin Alix: Executed March 30, 2010; Age 34
Robert Coulson: Executed June 25, 2002; Age 34
Luis Salazar: Executed March 11, 2009; Age 38
Allen Janecka: Executed July 24, 2003; Age 53
Mathis Milton: Executed June 21, 2011; Age 32
Vincent Gutierrez: Executed March 28, 2007; Age 28
Edgar Tamayo: Executed Jan. 22, 2014; Age 46