McCarthy, 26, only spent one season at Palace, following a move from QPR last summer, and signs a three-year deal with the Saints.
Pied, 27, played for new Southampton boss Claude Puel for Nice last season, as well as working under him at Lyon.
He has signed a two-year contract with the south coast club.
The Saints have now made four signings this summer, following the arrivals of Nathan Redmond from Norwich and Pierre-Emile Hojbjerg from Bayern Munich.
McCarthy, who only played seven times for Palace, will compete with England international Fraser Forster for a first-team place at St Mary's.
"The club is known for producing young players and they've had successful seasons," the former Reading keeper said.
"There's the Europa League to look forward to this season, so there are going to be a lot of games."
Pied, who can also play on the wing, said: "I am very happy to be able to join this new team. The English league is a very attractive one and it was a goal of mine to be able to play in it."
Southampton have signed Crystal Palace goalkeeper Alex McCarthy for an undisclosed fee and French right-back Jeremy Pied on a free transfer.