The Lions forward, 25, will play in the Challenge Cup semi-final in Montpellier despite injuring his eye in the derby defeat at Cardiff Blues.
Faletau's inclusion means the Dragons are unchanged from the team that beat Gloucester in the quarter-final.
The Dragons are hoping to win a first title since becoming a region in 2003.
Faletau came off against the Blues but the 57-cap back-rower has been passed fit for the Dragons' game in France.
Head coach Kingsley Jones is relishing the prospect of Faletau facing Montpellier's former South Africa number eight Pierre Spies.
"I know which number eight I prefer to have playing for us and that's Taulupe Faletau," said Jones.
Montpellier are second behind Clermont Auvergne in the French Top 14 table while only Italian clubs Zebre and Treviso are below Dragons in the Pro12.
Dragons have lost their last eight Pro12 games but shocked defending Challenge Cup champions Gloucester in the quarter-finals.
It is the first game for the Welsh region since their director of rugby Lyn Jones departed, and Kingsley Jones will take charge of the team following a disrupted build-up.
Former Wales Under-20 international Jack Dixon returns to the replacements' bench as the 21-year-old centre has recovered from a kidney injury.
Montpellier: Benjamin Fall; Timoci Nagusa, Robert Ebersohn, Frans Steyn, Marvin O'Connor; Demetri Catrakilis, Benoit Paillaugue; Mikheil Nariashvili, Bismarck Du Plessis, Jannie Du Plessis, Robins Tchale Watchou, Paul Willemse, Fulgence Ouedraogo (capt), Akapusi Qera, Pierre Spies.
Replacements: Mickael Ivaldi, Yvan Watremez, Davit Kubriashvili, Thibaut Privat, Wiaan Liebenberg, Nic White, Benjamin Lucas, Anthony Tuitavke.
Dragons: Carl Meyer; Adam Hughes; Tyler Morgan, Adam Warren; Hallam Amos; Dorian Jones, Sarel Pretorius; Phil Price, Elliot Dee, Brok Harris, Rynard Landman, Nick Crosswell, Lewis Evans (c), Nic Cudd, Taulupe Faletau.
Replacements: Rhys Buckley, Boris Stankovich, Lloyd Fairbrother, Matthew Screech, Ed Jackson, Charlie Davies, Angus O'Brien, Jack Dixon.
Referee: Wayne Barnes (England)
Assistant referees: JP Doyle, Greg Garner (England)
TMO: Rowan Kitt (England)
Citing commissioner: Alberto Recaldini (Italy)
Wales number eight Taulupe Faletau has been passed fit for Newport Gwent Dragons' attempt to qualify for their first European final on Saturday.