President of the Jamaat Sajjad Manji said his group had gone largely unnoticed because it had a great relationship with its neighbours.
"We've been here for donkey's years," said Mr Manji, a pharmacist who lives on the Tile Kiln Estate, near Galleywood.
"We're a small community and we've been here a long time – we've never had a problem with anyone."
Some members' families came to this country after fleeing Uganda and Tanzania in the 1960s, he added.
In 1978 a number of them began to open their homes to other Muslims, providing places to meet and pray.
These families then became the Jamaat of Essex and after a brief spell of hiring the Brentwood Co-op Hall, opened a permanent place of worship in Regina Road in 1989.
But soon the tiny house became too small for their needs – regularly accommodating more than 100 members in a building that could cope only with 70 people.
"We are all very pleased. The need for a new Islamic Centre cannot be underestimated for our community. We just need the space," Mr Manji said.
The old building will be replaced by a four-storey centre that includes two prayer halls, accommodation for guest lecturers and a school for 30 children.
Councillor Ron Alcock, who supported their cause, said: "They have been trying to find another location to congregate for years because that place was just too small.
"It's great news."
As well as a mosque and a Muslim community centre, the building will be able to accommodate other local groups.
Source: Vinienco