The 31-year-old, who came third in BBC One show Strictly Come Dancing, has been dating Jones, 27, for eight years.
Bunton, commonly known as Baby Spice, said: "I guess I will be handing over the 'Baby' tag now to a deserving little new owner."
It is thought the baby is due sometime in the summer.
In a statement, the couple said: "We are so happy, it's unbelievable news. What a great start to the New Year."
Bunton recently revealed she been had diagnosed with endometriosis, a condition which can make it difficult to conceive.
In a magazine interview last month, she said: "I went back to my doctors recently, and they seemed to think it was easing off, which would make it hopeful for me to have children."
Bunton recently reached number three in the charts with her own version of the '60s classic Downtown, for Children in Need.
Bunton is not the only pregnant Spice Girl, as Mel B is expecting her second child in the spring.
She says the father is actor Eddie Murphy - but he has demanded paternity tests.
Geri Halliwell gave birth to her first child, Bluebell Madonna, eight months ago and Victoria Beckham has three children, Brooklyn, Romeo and Cruz.