Pelosi, who joined the Reds two years ago, has agreed to a contract extension, while Brannagan has earned his first professional deal after a number of impressive performances for the club's under-21 side.
Highly regarded USA youngster Pelosi has been out since February after sustaining a broken leg against West Brom, but has progressed well enough in his recovery for Liverpool to show faith in him with a new deal.
The 19-year-old arrived at Liverpool from California-based DeAnza Force after impressing Anfield scouts during the under-17 World Cup, during which he captained his country into the last 16.
Pelosi was willing to forgo the opportunity to attend college in the US in favour of signing for Liverpool, and is among several young talents edge towards a future spot in Brendan Rodgers' first-team.
Brannagan, meanwhile, continues to progress in the under-21 squad and the agreement of pro-terms comes after some memorable performances this term, during which time the 17-year-old has scored against Tottenham and Manchester City.