A task force of 28 local elected officials voted unanimously for the plan Friday night.
The plan now goes to the local school board and ultimately will have to be approved by residents at a referendum.
If all goes well, officials said construction could begin in the spring of next year and the new building could open in January 2016.
On the morning of Dec. 14, gunman Adam Lanza, who had killed his mother at their Newtown home, went to Sandy Hook Elementary School and opened fire with an assault rifle, killing the 20 children and the six adults. He killed himself as police arrived at the school.
The school shooting, one of the deadliest in U.S. history, has spurred national debate about gun control and Second Amendment rights.
Police have not disclosed possible motives for the Newtown killings. Law enforcement officials have said Lanza showed an interest in other mass killings and played violent video games.
The Associated Press contributed to this report.