Penny Roberts had been warned that the social services department at Bradford council was considering taking the child into care because of her disability.
Ms Roberts, a 35-year-old former nurse from Keighley in West Yorkshire, conceived the child last January.
She had feared that her disability would prevent her from having children.
She and the father, then her fiance, Andrew Mitchell, separated shortly afterwards, but before either knew that she was pregnant. The decision by Bradford to offer support for her to care for the baby herself came after a case conference yesterday that involved both parents.
Ms Roberts had initially declined to name the father.
Mike Stow, assistant social services director, said last night: "Every parent faces numerous challenges when raising a child, and because of her disabilities Miss Roberts will encounter many additional difficulties. But I am sure that with her level of commitment and determination she will more than meet the challenge.
"This has never been an issue of cost but a genuine desire to provide the best possible upbringing for this child."
Ms Roberts has used a wheelchair since losing the use of her arms and legs after the accident in Florida when she fell 14,000 feet as her parachute failed to open properly and the emergency parachute became tangled.
She is looked after at home by a team of carers at a cost of pounds 500 a week and wants more support from social services to help her to establish a routine with the baby, she has said.
After the case conference, Mr Mitchell said: "Social services have acted quite responsibly in making an assessment in order to arrive at the decision to let Penny care for the child."
Ms Roberts was yesterday unavailable for comment.