Jamaican Bucknor was dropped by the International Cricket Council (ICC) during the four-Test series in Australia last month following pressure from India, who had criticised his performance in their 122-run defeat against the hosts in Sydney.
Bucknor will stand in with Pakistan's Alim Dar in the first and second Tests between Bangladesh and South Africa, starting on February 22 and 29 respectively.
India had also accused Bucknor of playing a major role in the row over their spinner Harbhajan Singh, who was charged with racially abusing Australia's Andrew Symonds, a charge which was later dismissed by an independent judge.
The decision to drop Bucknor was one of the factors which allowed the Australia tour to continue after India's cricket board had threatened to take their team home.
Bucknor has umpired a record 120 test matches, as well as 167 one-day games.
Only David Shepherd of England and Rudi Koertzen of South Africa have umpired more one-day internationals.
The 61-year-old Bucknor has also stood in five successive World Cup finals.