The 21-year-old arrives at the Emirates Stadium on a five-year contract and is manager Mikel Arteta’s first summer signing.
Tavares is expected to provide competition for Scotland international Kieran Tierney at left back and will don the number 20 jersey.
He broke into the Benfica team at the start of the 2019/2020 season and made 41 appearances in total for the club before his departure to England.
"When I finished the season my agent told me that Arsenal were interested in me," Tavares told the club's official website.
"In the first instance I was very happy and after this I dreamed about it, and [spoke about it] with my mum. I was so excited to be here, and now I'm here I'm so happy.
"I'm so excited because it is a big club and for me as a young guy, it is a pleasure to be here.
"Mikel [Arteta] and Edu helped me so much. They speak with me every time, and call me and I feel people want me here. I like that because I need this power and I'm so grateful for this."
Arteta added: "We welcome Nuno to the club."
"He is a young player with great promise who has developed very well with Benfica in recent seasons and has also shown his quality by being part of Portugal U21s.
"Nuno's arrival will give the squad extra strength and options in defence, particularly with this energy on the left side of the pitch.
"We look forward to Nuno's arrival soon, his integration into the Arsenal family and playing in front of our fantastic supporters."
