Weca, which manages regional planning, transport, housing and adult skills training, was formed by Bristol, South Gloucestershire, and Bath and North East Somerset councils in 2017.
They, along with North Somerset, used to make up a single authority – the County of Avon, a controversial merger created in 1974.
It was dissolved in 1996, creating four unitary authorities, three of which later decided to join together to create Weca.
North Somerset opted out, but a formal application to join was submitted last year.
A public consultation on the plans was later opened, with more than half of those taking part saying they supported the idea.
Subject to approval by the secretary of state and legislation being passed, North Somerset could become a full member of Weca from late 2026 or early 2027.