The Spanish giants are still reeling from the departure of Lionel Messi, who joined Paris St Germain after the club were unable to honour a new contract because of financial restrictions.
Barcelona confirmed all of the three new players would be available for Sunday's opening LaLiga fixture against Real Sociedad.
However, free signing Sergio Aguero - who left Manchester City at the end of last season - is still recovering from a calf problem and is set to be sidelined for up to 10 weeks.
Barcelona were able to reduce their wage bill following the sale of Junior Firpo to Leeds and Francisco Trincao's loan to Wolves, while Jean-Clair Todibo joined Nice, Carles Alena went to Getafe and Konrad De La Fuente joined Marseille.
A statement on the club website read: "Barcelona is able to register Memphis, Eric Garcia and Rey Manaj to play in the Spanish Liga de Futbol Profesional. This has been made possible thanks to an agreement with Gerard Pique whereby the Barca second captain's salary has been substantially reduced.
"This means that all of the first-team players will be available for selection by Ronald Koeman for this Sunday's opening Liga fixture against Real Sociedad.
"The club is also continuing to work with two of the other captains, Sergio Busquets and Jordi Alba, to adapt their salaries to the club's current situation. It must be noted that both players are totally and utterly willing to cooperate.
"This summer, FC Barcelona has achieved a number of sales and loans with regard to its senior squad that have meant that all of the players can be registered for the start of the 2021/22 season."