Lazio's decision to sell the former Arsenal midfielder has angered coach Maurizio Sarri, who spoke out against the sale.
Guendouzi has penned a four-and-a-half year deal.
Speaking after his switch was made official, he said: "I am truly very proud. I am very happy to be here today. I really wanted to be here. That's why I'm so happy, this is a big day for me and my whole family. I'm enjoying this moment. I hope we will achieve great things together.
"First of all, I want to thank everyone who contributed to this transfer. Because it wasn't an easy process. From the moment I first heard about it, I really wanted to come here and I did. I am very proud and Fenerbahçe is one of the biggest clubs in the world, with a great history.
"Our president also told me about our club, our fans and our goals. I am very happy and excited to be here. I know our fans and the great atmosphere they create, I can't wait to play my first match in front of them. I hope we will win victories and trophies together here.
"I want to thank our fans. Because I received many loving messages from them on social media. They can be sure that I will give everything on the field for them if necessary. I am always that kind of player. I hope we win the league championship together after 12 years. I hope we can achieve our goals together with our fans, our team, and our coach."