Dr Nagpaul will take over the post from Dr Mark Porter, whose five-year term as chair ends on Thursday 29 June 2017.
The north London GP of 27 years said it was a 'tremendous privilege and honour' to lead the medical profession.
He said: 'The challenges facing doctors and the health service in which we work have never been greater. Doctors are at the sharp end of chronic underfunding, staff shortages and rising demand on the NHS, and see first hand the devastating impact these pressures have on patient care.
'I will work to ensure that the BMA supports doctors facing these pressures, and will lead the charge for an NHS that is properly resourced by the next government, so that doctors can provide the safe, high-quality care patients deserve.'
Dr Nagpaul, who in 2015 was awarded a CBE for services to primary care, paid tribute to the hard work and leadership of his predecessor Dr Porter. 'The BMA has always proven itself to be a strong, independent voice for both doctors and the patients we serve and with the NHS at breaking point, this is more important now than ever in holding politicians to account,' he said.
'I look forward to continuing with this vital work at a pivotal time for doctors across the profession and for the NHS as a whole.'
News of Dr Nagpaul's election win was broken on Twitter by GPC member Dr Krishna Kasaraneni.
Dr Nagpaul, a GP in Stanmore, north London, was elected chair of GPC in 2013 and led the profession through the turbulent period following the health and social care act reforms and the funding, workload and workforce crises in general practice.
Under his leadership the GPC last year secured a rescue package for the service in the form of NHS England's £2.4bn GP Forward View. In one of his most outspoken speeches at the annual conference of LMCs in Edinburgh last month Dr Nagpaul hit out at politicians' 'callous disregard for the NHS' and called on GPs to 'stake our claim with our patients and the public to demand that the general election delivers a government that will fund the NHS properly'.
He told LMC representatives that despite extra funding delivered through the 2017/18 GP contract deal and pledges set out in the GP Forward View, the service remains in a parlous state and on the brink of collapse, with thousands of practices unable to recruit and many warning they are struggling to remain financially viable.
However, he said, the GPC had secured advances for the profesion, with NHS England's acceptance that to take forward the Urgent Prescription for General Practice, and the 2017/18 contract which ended the avoiding unplanned admission enhanced service, with t£157m put into core funding, and practices freed from the bureaucracy of care plans.