The 22-year-old, born in Burundi to parents from Rwanda and DR Congo, has been given a Rwandan passport.
He is now expected to feature in their forthcoming African Cup of Nations qualifiers.
Tchite plays for Belgian first division side Standard Liege and is expected to be a major addition to the squad.
Scoring 16 goals in 33 games for the Belgian league runners-up, Tchite had played for local side Mukula FC before going to Belgium.
« He went to Belgium on a Congolese passport because he had problems with our FA, » explained Rwanda assistant coach Batista Kayiranga
« But now we have sent him our passport and he is ready to play for us. He has a lot of experience in competitive football. He will fortify our attack. »
Rwanda, now being coached by German Michael Nees, played a friendly match against Tanzania on Sunday, which they lost 1-0.
Tchite is not the only one to opt for Rwanda, as other DR Congo-born players and a Kenyan have switched allegiance.
Striker Abeid Mulenda, who earned his second cap against Tanzania on Sunday, as well as midfielders Mutessa Mafisango and Bob Rafik are of Congolese origin, while goalkeeper Ben Mandela is from Kenya.
« It doesn’t matter (changing nationality) because we have seen players playing for their junior teams and then switch to play for another country at senior level, » Mandela told BBC Sport.
« In life sometimes you have to use short-cuts. Rwanda is a nice place, they have welcomed me and I am happy there. »
BBC Sports
NB: Rwanda vs Cameroon, 03/09/2006 Kigali