Patricia Connors and her pet died after it ran on to the carriageway near Cardiff Gate services on Friday at about 18:20 BST.
In a statement, her family said they were "heartbroken".
The westbound carriageway was closed for five hours between junctions 29 and 32.
Ms Connors was pronounced dead at the scene.
Her family said they were trying to come to terms with what had happened and described her as a "loving mum, grandmother and great-grandmother".
Tributes have been paid to a 66-year-old woman who died after she was hit by a van while trying to save her dog after it got loose on the M4.