Pellegrini joins from Estudiantes as a Young Designated Player, while Carranza arrives from Banfield.
Both 19-year-old Argentina youth internationals will return to their respective clubs on loan until January.
They are the first players to be signed by the Miami franchise, which will debut in MLS in 2020.
"It's important for us that we found young, exciting attacking players that are on the upside of their career and have the potential to be really good players in this league," Inter Miami sporting director Paul McDonough said.
"We will continue to build and add quality players that are the right fit for our club. We started with youth, but we know it's also important to have veteran players who come from both overseas and within the league to balance out the roster over time.
"Both Julian and Matias showed us they really wanted to take the next step of their career with Inter Miami. We liked that Pellegrini can play inside and out wide, has very good aerobic capacity and can cover a lot of ground, while Julian is a very grounded player with an impressive work rate. He's the player that strives to score goals and is very good in the box."