The 34-strong BMA Council backed Dr Meldrum ahead of two other prominent GPs on the day that Alan Johnson became health secretary. The vote took place on 28 June at the BMA's Annual Representative Meeting (ARM) in Torquay, Devon.
Chairman of BMA Wales and the BMA ethics committee Dr Tony Calland and East London GP Dr Sam Everington were the other candidates.
Dr Everington had been acting BMA chairman since the resignation of Mr James Johnson in May. He now returns to the post of deputy chairman.
Mr Johnson quit after a letter he wrote to The Times newspaper angered junior doctors because it failed to reflect their outrage over the Medical Training and Application Service fiasco.
Dr Meldrum works one day a week as a GP in Bridlington, East Yorkshire, where he has practised since 1978. He was chairman of East Yorkshire LMC from 1996 to 1999, and was part of the GPC negotiating team that agreed the new GMS contract.
'I'm very pleased. It's going to be a difficult job, and I have lots to learn about some of the non-GP areas of the role,' Dr Meldrum said.
Asked what he would bring to the BMA role, Dr Meldrum said: 'I think I've shown in the past years with the GPC that I can communicate well with and on behalf of the profession.'
Dr Meldrum would not reveal details, but said he had ideas on improving the BMA internally to make it more effective and seem more relevant to its members.
His first task in his new role had been to write to the new health secretary to congratulate him on his appointment and to ask for a meeting in the near future, Dr Meldrum said.
A new GPC chairman will be elected on 19 July, and acting GPC chairman Dr Laurence Buckman said he intended to stand for the permanent post.
He predicted at least five candidates would contest the election. Each will publish a one-page manifesto in the run up to the contest, and rounds of voting will take place until one candidate has a clear majority.
Dr Buckman said of his candidature: 'I want to give GPs hope, and the belief it can get better than this. I want them to feel valued, and not just in cash terms.
'We need to stop being defensive and go out there and say what a fantastic service we provide.'
Comment below and tell us what you think