The boys were delivered by emergency caesarean in January, six weeks before they were due.
They were conjoined at the base of their spines and gastrointestinal tract and had to be separated because of the severity of Jacob's heart condition.
Now eight months old, Jacob and Joshua, from Memphis, Tennessee, were operated on at Le Bonheur Children's Hospital in Memphis, the same hospital in which they were born.
The boys' delighted mother, Adrienne Spates, said the babies are doing well since their operation, on August 29.
Dr Max Langham, one of the surgeons at Le Bonheur Children's Hospital in Memphis, said: 'Joshua's doing great, and hopefully he'll be up and going and have a pretty normal lifespan.
He said that while Jacob has more serious heart problems, 'our cardiology team has very high hopes his treatment... will be successful'.
'If they had not been separated, sometime in the next year or two, they probably would have passed,' Dr Langham said.
* Just two dozen conjoined twins have ever been successfully separated worldwide.
* The condition is extremely rare, only about one in every 200,000 live births is a set of conjoined twins and about 15 per cent of these are joined in a similar way to Joshua and Jacob.
* Fewer than a third of conjoined twins survive more than one day.
* Before the operation doctors practiced how to separate the twins successfully, including the anaesthesia team sewing together two Cabbage Patch dolls to practise flipping them without tangling the various lines that would be attached during surgery.
More:Advice And Health
Suggested For You
SUBSCRIBE AND FOLLOW
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements.Learn more