The delay in the completion of the deal - caused by the late arrival of documentation from France - is expected to be a minor one after Lyon finally gave the go-ahead for their prize asset to leave for the Premiership.
The midfielder is already good friends with Drogba, who made his £24m switch to Chelsea from French side Marseilles last summer and expects Essien to settle in quickly at Stamford Bridge.
"He does not need any advice from me about English football because he is very strong, very powerful and has all the qualities to play in England," the Ivory Coast striker said.
"He really wants to come and so it will be easy for him to come into a big squad like Chelsea. Everybody is waiting for him and he will give us a lot."
Essien is unfazed by the challenges which adapting to English football is likely to bring.
"This is a new adventure," he declared. "I am not scared about it. I know where I am going. When I signed with Lyon, I knew there was a lot of competition in midfield too and it was not always easy.
"But I fought to earn my place and I will do the same in London. It is that competition which allowed me to progress and thanks to that Chelsea spotted me."
Essien joined Lyon from Bastia in 2003, and became an integral part of their side, but missed the four-time defending Ligue 1 champions' opening three matches of the season because of the Chelsea transfer saga.
"I would like to thank the president and the technical staff [at Lyon] for allowing me to make my dream come true - this is great," he added. Lyon did all they could to keep me, but going to Chelsea is just too crazy [to turn down].
"I really like the English Premier League. I wanted to play in it and Chelsea have become one of the greatest clubs in Europe."
The arrival of Essien will certainly hand the Chelsea manager Jose Mourinho an extra dimension to his midfield options, with Eidur Gudjohnsen now set to revert to a more familiar role of striker rather than supporting the frontman as he did against Wigan last weekend.
The Iceland international failed to have a major impact on Sunday and was replaced at half-time by England's World Cup hopeful Joe Cole.
With Arjen Robben and Shaun Wright-Phillips, who missed England's friendly with Denmark last night because of a swollen knee, also having 45 minutes each as Chelsea struggled to a stoppage-time, 1-0 victory over the Premiership newcomers, Mourinho has warned he will not be afraid to shake things up as he prepares for the much-anticipated showdown with Arsenal at Stamford Bridge this weekend.
However, the match against the Gunners is likely to come too soon for Wayne Bridge, who played in a reserve-team run-out against Tottenham on Monday. It was the first 90 minutes of competitive football the left-back has played since breaking his ankle in February.
Essien's imminent arrival could result in the Czech Republic international Jiri Jarosik following Russian Alexei Smertin on a season-long loan deal away from west London, with Birmingham City said to be tracking his availability.
Chelsea have also announced that there will be extra security measures in place for Sunday's match with Arsenal, including searches at the turnstiles.
Supporters are being urged not to bring any rucksacks or large bags into the stadium to help speed up entry.Reuse content