The former Manchester United and Molde manager has signed an 18 month deal with the Black Eagles.
At his presentation on Sunday, Solskjaer said: "I actually had other offers, but I had a good life in Norway. There had to be an offer that was worth giving up my life for. Istanbul is a fantastic city, I couldn't say no to this offer. If I hadn't accepted, I would have regretted it long before I died.
"The project here is similar to that of Manchester United. At United we also finished the season in sixth place, and then we grew step by step. We want to win, but we also want to be realistic. We have to stop the negative trend."
Solskjaer also said: "I haven't spoken to José Mourinho (Fenerbahce coach) yet. He is an extraordinary manager, a name that has achieved a lot of success. I can't wait to meet him again and I have great respect for him."
He continued: "We had excellent meetings with our president and we also found each other on a human level. The bonds that we will build in this team are very important. Here we will build a new base. This was something I really wanted. Our president touched my heart and that of the technical staff.
"While I worked at UEFA (as a Match Analyst.), I followed the games and Beşiktaş. I am proud to be in a club like this.
"I know what the fans want. We will work every day for this. I am here only to win. We have players who are used to winning. Beşiktaş is a team that deserves victories. I have always aimed for this both as a player and as a coach, and that is why I came here."