Eto'o and Mbia missed Cameroon's final pre-tournament friendly against Moldova due to fitness concerns - although some had claimed they were on strike due to a disagreement with the Cameroonian Football Federation (FCF) - but Finke claimed they would be ready to play Mexico.
With hosts Brazil overcoming Croatia 3-1 in the other Group A encounter on Thursday, any winner from Cameroon against Mexico would take a significant step towards the round of 16.
Finke underlined the importance of striker Eto'o and defensive midfielder Mbia ahead of Friday's clash at Natal's Arena das Dunas.
"I'm happy that Stephane Mbia and Eto'o are back in the team - that's very important for us," Finke said at his press conference on Thursday.
"They give a lot to the team and they're the kind of players that can make the difference."
Finke was also relieved that the pay dispute between his 23-man squad and the FCF had been resolved.
Reports had suggested the likes of Eto'o, Mbia and Alex Song had been the ringleaders of the players' strike and that players had threatened not to get onto their flight to Brazil if their demands for pay bonuses had been ignored.
But Finke declared the situation had been resolved.
"Here (in Africa) we have traditions, there are certain relationships with the football federation and the government. You have to respect certain ways," the German coach said.
"It's not like in France or Germany. From my point of view, I see a team that is working very hard. For everything else, I say we have to step back and respect their ways.
"We have found a solution, and that is the most important thing."
Cameroon - at 56 - are the lowest-ranked team in Group A and have only reached the knockout stages at one of their six previous appearances at World Cup finals.
The African nation failed to claim a point in South Africa four years ago and defender Nicolas N'Koulou said Cameroon are desperate to show the world they can compete this year.
"We're coming here with a feeling of revenge, that's for sure," the 24-year-old said.
"We totally failed in 2010 but things are different now. We're a cohesive group and have a good mix of experience with some younger players.
"We're like a family. We're in good spirits and determined to give it everything to make the nation proud."
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