Support from Wandsworth LBC's Housing Overview and Scrutiny Committee follows a public consultation although it has to be discussed by the executive on 24 November.
Around 17,000 letters were sent out to tenants formally notifying them about the proposed scheme but nobody who responded opposed it.
The new rules will mean that all new tenants must have their animals chipped as part of their tenancy agreement.
The rules will apply to new tenants from 5 January. Existing tenants will have until June, a year after the scheme was first announced, to get their pet chipped before enforcement action is taken.
Micro-chipping will be offered free-of-charge to tenants and leaseholders.
The council says an estimated 4,000 dogs live on the borough's estates.
Recording ownership details on a database will help the council deal quickly with strays and take action against tenants who allow their dogs to cause a nuisance.