The two groups, which together own more than 32,000 homes, say the merger has been approved by the Homes and Communities Agency.
Bosses say Thirteen Group will have a turnover of about £140m a year, becoming the North-East's largest registered housing provider.
They added the move will see Fabrick and Vela's partner companies, Erimus Housing, Tees Valley Housing, Housing Hartlepool and Tristar Homes, remain as separate organisations, but becoming part of the larger group.
In the move, Alison Thain, Fabrick chief executive, will become chief executive designate of Thirteen Group, with Cath Purdy, Vela chief executive, taking on the role of chief operating officer designate.
Ms Thain said: “We are thrilled to announce we will become Thirteen Group, a name testament to the company’s vision of doing things differently and pioneering new ways to deliver homes and create sustainable communities.
“Joining forces gives us an exciting opportunity to build on Fabrick and Vela’s achievements by challenging and looking at things differently, to act with confidence and ambition for the benefit of the individual, the Tees Valley area and wider region.”
The changes also include plans to create Thirteen Care and Support, a housing support division bringing together the services of Tees Valley Housing and Norcare, the Tyneside-based charity part of Fabrick Housing Group.