The 16-year-old Londoner had her money temporarily suspended in December after the governing body claimed she had arrived at a training camp overweight and without an acceptable training plan.
BWL's performance management group have now reversed that decision after noting "a number of positive changes".
Earlier this month Smith, who came third in the Commonwealth Games in Delhi last year, finished second in the Tri-Nations tournament in Norway despite being on the comeback from injury.
"I am so pleased to hear that what I consider to be the right decision has been reached," she said.
"I have ensured over the last two months that I have met the requests of the governing body in terms of submission of my training diaries and personal contact with them.
"But in terms of training, performance and commitment to my sport, I have never, at any point, shown a drop in my enthusiasm or dedication to succeed.
"It has been a really difficult time.
"I've had to balance the pressures of both school and training with the huge amount of media interest.
"I'd like to thank everyone who showed me support throughout the period in which my funding was suspended, for genuinely helping me to get through it.
"The kindness of the public has been heart-warming and I'm now even more determined to succeed in my sport and represent my country to the best of my afbility to say thank you to everyone who has shown that belief in me."
Fiona Lothian, BWL's performance manager, welcomed the decision.
"I am pleased with the progress Zoe has made since Christmas, she is adhering to a structured programme and her training is back on track," she said.
December 2010: Alan Hubbard - Zoe Smith deserved a prize from British Weight Lifting not a kick in the teeth
December 2010: British Weighlifting withdraws funding to top Olympic prospect after they claim she is overweight