Here are the (complex, confusing) rules around executions in each state. We've given Tennessee a slightly different treatment, but it's generally similar to states nearby.
Most states default to lethal injection. And as data from the Death Penalty Information Center shows, most of the executions since the Supreme Court lifted a ban on the the death penalty in the 1970s have been by lethal injection. But by no means all.
What's particularly interesting is to see how the method of execution has evolved over time. Using data from a 2002 paper by Fordham Law School professor Deborah Denmo, we graphed the evolution in methodology, by state.
In every state, the preferred method of execution was once hanging. Then, during the 20th century, states tended to shift toward the gas chamber or electric chair. Injections are new; Oklahoma was the first to make it the default means of execution.
Tennessee's new law, then, isn't really new. If anything, it's a reversion to what was once the norm.