Eriksson, who guided England to the quarter-finals in 2002 and 2006, replaced previous incumbent Vahid Halilhodzic, who was sacked following the disappointing quarter-final exit in the African Cup of Nations in January.
"Eriksson is one of the best managers on the market and has done a lot of good things with the England national team," added Drogba in an interview on BBC World Service.
"He is a very good professional and with his experience I hope we can beat one or two big teams at the World Cup.
"He knows there is a lot of work to do that's why he started very quickly when he got the job."
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