The Gunners confirmed on Saturday that Tavares had joined on a long-term deal, with Arsenal having paid the Primeira Liga side a reported €8million plus add ons.
Left-back Tavares made 25 league appearances for Benfica, 17 of which were starts, and proved himself an impressive creative outlet.
Indeed, Tavares created 23 chances in the Portuguese top flight, laying on four assists.
He will link up with the Arsenal squad after travelling from Portugal and completing his period of isolation in the United Kingdom.
"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.
"[Manager] Mikel [Arteta] and [technical director] 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 said: "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 Under-21s.
"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."