The 11-to-10 vote on Tuesday came after lengthy and sometimes emotional debate from both supporters and opponents of the death penalty.
Before debating the bill, senators voted overwhelmingly to remove a provision to spare the lives of 17 killers already on death row, a point of contention for some lawmakers.
The measure, opposed by Attorney General Beau Biden, now goes to the state House for consideration.
Gov. Jack Markell has refused to say whether he favors the legislation.
Supporters of the bill argue that the death penalty is morally wrong, racially discriminatory and ineffective as a deterrent to violent crime.
Opponents argued that some murders are so heinous and atrocious that capital punishment is appropriate.