A 17-year-old suspect, who was from the Calne area and was known to Ellie, was remanded in custody ahead of a court appearance at court on Tuesday, police said.
Ellie, a student at Hardenhuish School, was pronounced dead after emergency services were called to a house in Springfield Drive in Calne at 3.15pm on Friday.
Police detained the suspect in the nearby town of Chippenham later that afternoon.
Inspector Don Pocock said: “A case like this takes time and will understandably have an impact on the local community – so thank you for your help and understanding.
“Over the past few days, people living in Calne and Chippenham would have seen an increased police presence which I appreciate can add more anxiety and upset to what is already a tragic situation.
“However, I want to reassure everyone that the officers and detectives involved have been working hard to carry out their duties as swiftly as possible to minimise the impact on those living and working here."
The teenage boy cannot be named for legal reasons and will appear before Salisbury Magistrates' Court on Tuesday.
Lisa Percy, head teacher of Hardenhuish School, said: “I would like to thank everyone for all of the messages of support that we have received from past, present and future parents, colleagues and other members of the community.
“We would like to express our thanks to all partner agencies who have supported us too.
“The students, staff and parents have found comfort in being together and paying their respects to Ellie and our thoughts remain with her family and friends at this time.”
Anyone with information is asked to contact Wiltshire Police on 101, quoting log number 176 on May 3.