Kjaer joined Sevilla on a four-year deal on Wednesday after arriving from Turkish giants Fenerbahce for €12.5 million – making him the club's most expensive defender.
The 28-year-old centre-back became a cult hero in Istanbul but he is now aiming high at Sevilla, who finished fourth in La Liga last season as they qualified for the Champions League play-off round.
"Sevilla are a top club in the best league in the world, and it is a club with ambitions of making a mark in the Champions League and in La Liga -and they are used to winning titles," Kjaer told Omnisport.
"The club's achievements in the Europa League in the recent decade or so have been absolutely outstanding and calls for a lot of respect, and we must continue to deliver results to that high standard."
"I have been touched by the emotions and incredible amount of reactions for example on Twitter from Fenerbahce supporters," Kjaer continued. "They have been fantastic to me and my family, but the football world and a football career is like that. I have enjoyed the passion of the Fenerbahce supporters, and it is true, that they will always have a place in my heart.
"But I know, that I have moved to a club with supporters also famous for their passion and the support for the team. I am sure, that the first time I enter Ramon Sanchez Pizjuan will be an unforgettable moment, and I can't wait to get started."
It has been a busy close-season for Sevilla, who replaced former head coach Jorge Sampaoli with Eduardo Berizzo, while they have also signed Luis Muriel, Ever Banega, Nolito, Jesus Navas, Sebastien Corchia and Guido Pizarro.
Kjaer added: "The city and the club have received me with open arms, and not only the weather is extremely warm here but also the passion for football and for the club. I love that. And it is one of many good reasons to move to Sevilla.
"I play football with my heart, and that is what it's all about here in Sevilla: Passion. It is also a great city to live in for my family, but first of all I chose Sevilla because of my football ambitions.
"For my football and for my family this is the best move that I have ever made in my career. I come to a club with a lot of ambition, a great style of football and an extraordinary winning mentality. There is a great coach in Berizzo and a lot of top class players, and I have already experienced the very high quality of our training.
"I consider La Liga the best league in the world, when you speak about quality. How could anyone doubt that when you look at the results and triumphs in the European competitions in recent years of the Spanish clubs - like Sevilla in Europa League? La Liga is the place to be in football, and I believe that Sevilla are the perfect match for me."
The pair spent one season together at Lille before Kjaer left for Fenerbahce in 2015.
"It felt great to be welcomed by a good friend in football, Sebastien Corchia," Kjaer said. "We had a good time together in Lille, and now we meet again in Sevilla.
"I also know Michael Krohn-Dehli very well from the Denmark team, and of course I received some extremely positive information about the city and the club before I came here. Also from the former Sevilla player and my colleague from the Denmark team, Christian Poulsen."