The 34-year-old midfielder had just landed in Cape Town when he was told the news by distraught family members.
Beckham was extremely close to Joe, who was 83, and often cited him as his footballing inspiration.
Close family: Grandparents Joe and Peggy were with Beckham and his wife Victoria when the midfielder was awarded his OBE at Buckingham Palace in 2003
Joe was the father of Beckham's mother Sandra, and the England international attended Tottenham's school of excellence under the guidance of his grandfather who was a huge Spurs fan.
Campaign: England's bid ambassador Beckham with FIFA chief Sepp Blatter in Cape Town
Beckham's family are believed to have urged him to stay in Cape Town, where he was due to take part in Friday's draw for next summer's World Cup finals and have crucial meetings with FIFA bosses to help England's bid to host the tournament in 2018.
Mr West's death follows a serious illness. In August, the Beckhams rushed back from LA after he was taken to hospital.
A friend said: 'David is absolutely devastated. He was so close to Joe, who was his mentor.
'Heonly got off the plane when he heard the news. His family are urginghim to stick to his work commitments and leave at the end of the week,but there is no way that David wants to miss Joe's funeral. If he hasto fly home, then so be it.'
Quality: Beckham played his part in the qualifying campaign for South Africa 2010
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