Caixinha, most recently in charge of Al Gharafa in Qatar, has signed a three-year contract at Ibrox to replace Mark Warburton, who left in chaotic circumstances last month.
Celtic's dominance of Scottish football has been unrivalled in the wake of Rangers being liquidated, reformed and forced to climb back up the divisions, starting from the fourth tier in 2012-13.
But in a dig at Brendan Rodgers' side, Caixinha says it is Rangers who are the biggest team in the Old Firm rivalry.
"We are talking about a worldwide club," he told Rangers TV.
"It is a massive club - the biggest club in Scotland. It is one club that is fighting to get on top again and we know we are going to get on the top.
"That is what we are here for, and the challenge is to help the club, to rebuild that path, the history and the glory – it is the main reason that brought us to this challenge."
Caixinha was pressed on his claim as he was unveiled to the media on Monday and responded by saying: "I give you two numbers - 144 years old and 54 league titles.
"That is more than enough. We trust the players we have right now. For us this is the best squad in Scotland and we just need to give them that confidence."
Caixinha watched Rangers' battling 1-1 draw at Celtic from the stands on Sunday and revealed his short-term targets include finishing second in the Premiership and tasting Scottish Cup glory this season.
The 46-year-old added: "In a massive club like this, I would identify three points - the history, the trophies and the fans.
"Regarding the goals, at all times we must focus on the trophies, and we are in the cup semi-final [against Celtic], so we need to think about winning that trophy.
"We need to think also about getting as close as possible to second positon in the league. We are now eight points below.
"You need to be ambitious, but you need to be realistic at the same time. We are being totally ambitious and realistic in saying that we would like to end up in the second position, and why not try to get a trophy in the Scottish Cup too?"