The 45-year-old Argentine replaces Claude Puel, who was sacked earlier this month after one season in charge.
Pellegrino stood down as Alaves manager in late May, after losing the Spanish Cup final to Barcelona and finishing ninth in La Liga with a club that had been promoted the season before.
"My philosophy and the culture of the club will work well," said Pellegrino, who has signed a three-year deal.
"I want to win matches, be successful and develop a team spirit where everyone gives 100% and supports each other.
"I am excited and passionate about what the future holds."
Southampton vice-chairman Les Reed said former Liverpool defender Pellegrino "impressed us with his depth of knowledge, motivation and ability", adding he "quickly became our first choice".
"While he had other options, we are delighted he feels that St Mary's is the right place for him," he added.
Saints finished eighth in the Premier League last season, losing 16 games, and also reached the EFL Cup final, their first major final since 2003.
Puel was the third manager to leave in the past three years, following Mauricio Pochettino's departure for Tottenham and Ronald Koeman's move to Everton.
His side were beaten 3-2 by Manchester United in the EFL Cup final in February, and they ended the season with just one win from their final eight league matches.
Pellegrino previously worked at Independiente and Estudiantes in Argentina, joining the latter after he was sacked by Valencia - his first job in management - following seven months in charge.
Prior to his appointment by the Spanish club in May 2012, Pellegrino worked as a coach under Rafael Benitez at Liverpool (2008-2010) and Inter Milan (2010).
As a player, he made 13 appearances for Liverpool in 2005 after being signed by Benitez, who he also played for during six years at Valencia from 1999.
He had arrived at Valencia from Velez Sarsfield, following a loan spell at Barcelona the year before.
He made three appearances for Argentina over the course of a 16-year career as a central defender that ended at Alaves in 2006.
Southampton have appointed Mauricio Pellegrino as their new manager.