Gwen Stefani has reportedly been discharged from hospital after giving birth to her second child with husband Gavin Rossdale.

No Doubt singer Stefani, 38, delivered her new baby boy, Zuma Nesta Rock Rossdale, by C-section at Cedars Sinai Medical Center in Los Angeles on Thursday.

Rossdale's father, Dr. Douglas Rossdale, tells U.S. magazine US Weekly: "Everyone is just so happy."

The rock couple's first son, Kingston, turned two in May.