Pellegrini signed a three-year contract last week to take over from Rubi, who was sacked last month after a string of poor results, and will start work at the end of the season.
Betis are currently being headed by Alexis Trujillo on a temporary basis, with the Andalusian club currently 13th on the Spanish La Liga table.
Betis’ solitary campaign in the Champions League came in the 2005/2006 season when they finished third in a group that included the likes of Chelsea, Liverpool and Anderlecht. They also made it to the knockout stages of the Europa League last season but were eliminated at the round of 32 stage.
Pellegrini is determined to secure European football for Betis next season after failing to reach that target despite splashing the cash on the likes of Borja Iglesias and Nabil Fekir at the start of the current campaign.
"Although the results have not been adequate, there has been institutional progress which must go hand in hand with the results on the field," Pellegrini said when presented to the media on Monday.
"We will contribute with our experience to get the best out of the team, to have committed players.
"It is everyone's job, we are on the same boat and the objectives are more feasible to achieve this way, with a winning mentality, because this is a team that should be fighting for European places."
He added: "I had other offers, but I preferred Betis because I believe in the club's project. They want to make Betis grow and they have done so, although perhaps not with the results on the pitch due to different circumstances."
Pellegrini took Villarreal to the semi-finals of the UEFA Champions League in the 2005/2006 season, losing to Arsenal and nearly replicated that feat with Malaga in the 2012/2013 season with a quarterfinal appearance.
